An Approach to Robust Control of the Hopf Bifurcation

Directory of Open Access Journals (Sweden)

Giacomo Innocenti

2011-01-01

Full Text Available The paper illustrates a novel approach to modify the Hopf bifurcation nature via a nonlinear state feedback control, which leaves the equilibrium properties unchanged. This result is achieved by recurring to linear and nonlinear transformations, which lead the system to locally assume the ordinary differential equation representation. Third-order models are considered, since they can be seen as proper representatives of a larger class of systems. The explicit relationship between the control input and the Hopf bifurcation nature is obtained via a frequency approach, that does not need the computation of the center manifold.

Stability and Hopf bifurcation analysis of a prey-predator system with two delays

International Nuclear Information System (INIS)

Li Kai; Wei Junjie

2009-01-01

In this paper, we have considered a prey-predator model with Beddington-DeAngelis functional response and selective harvesting of predator species. Two delays appear in this model to describe the time that juveniles take to mature. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. The stability and direction of the Hopf bifurcation are determined by applying the normal form method and the center manifold theory. Numerical simulation results are given to support the theoretical predictions.

Double Hopf bifurcation in delay differential equations

Directory of Open Access Journals (Sweden)

Redouane Qesmi

2014-07-01

Full Text Available The paper addresses the computation of elements of double Hopf bifurcation for retarded functional differential equations (FDEs with parameters. We present an efficient method for computing, simultaneously, the coefficients of center manifolds and normal forms, in terms of the original FDEs, associated with the double Hopf singularity up to an arbitrary order. Finally, we apply our results to a nonlinear model with periodic delay. This shows the applicability of the methodology in the study of delay models arising in either natural or technological problems.

Necessary and sufficient conditions for Hopf bifurcation in tri-neuron equation with a delay

International Nuclear Information System (INIS)

Liu Xiaoming; Liao Xiaofeng

2009-01-01

In this paper, we consider the delayed differential equations modeling three-neuron equations with only a time delay. Using the time delay as a bifurcation parameter, necessary and sufficient conditions for Hopf bifurcation to occur are derived. Numerical results indicate that for this model, Hopf bifurcation is likely to occur at suitable delay parameter values.

Local stability and Hopf bifurcation in small-world delayed networks

International Nuclear Information System (INIS)

Li Chunguang; Chen Guanrong

2004-01-01

The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis

Local stability and Hopf bifurcation in small-world delayed networks

Energy Technology Data Exchange (ETDEWEB)

Li Chunguang E-mail: cgli@uestc.edu.cn; Chen Guanrong E-mail: gchen@ee.cityu.edu.hk

2004-04-01

The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis.

Stability and Hopf Bifurcation Analysis on a Nonlinear Business Cycle Model

Directory of Open Access Journals (Sweden)

Liming Zhao

2016-01-01

Full Text Available This study begins with the establishment of a three-dimension business cycle model based on the condition of a fixed exchange rate. Using the established model, the reported study proceeds to describe and discuss the existence of the equilibrium and stability of the economic system near the equilibrium point as a function of the speed of market regulation and the degree of capital liquidity and a stable region is defined. In addition, the condition of Hopf bifurcation is discussed and the stability of a periodic solution, which is generated by the Hopf bifurcation and the direction of the Hopf bifurcation, is provided. Finally, a numerical simulation is provided to confirm the theoretical results. This study plays an important role in theoretical understanding of business cycle models and it is crucial for decision makers in formulating macroeconomic policies as detailed in the conclusions of this report.

Hopf bifurcation and chaos in a third-order phase-locked loop

Science.gov (United States)

Piqueira, José Roberto C.

2017-01-01

Phase-locked loops (PLLs) are devices able to recover time signals in several engineering applications. The literature regarding their dynamical behavior is vast, specifically considering that the process of synchronization between the input signal, coming from a remote source, and the PLL local oscillation is robust. For high-frequency applications it is usual to increase the PLL order by increasing the order of the internal filter, for guarantying good transient responses; however local parameter variations imply structural instability, thus provoking a Hopf bifurcation and a route to chaos for the phase error. Here, one usual architecture for a third-order PLL is studied and a range of permitted parameters is derived, providing a rule of thumb for designers. Out of this range, a Hopf bifurcation appears and, by increasing parameters, the periodic solution originated by the Hopf bifurcation degenerates into a chaotic attractor, therefore, preventing synchronization.

Hopf bifurcation and chaos from torus breakdown in voltage-mode controlled DC drive systems

International Nuclear Information System (INIS)

Dai Dong; Ma Xikui; Zhang Bo; Tse, Chi K.

2009-01-01

Period-doubling bifurcation and its route to chaos have been thoroughly investigated in voltage-mode and current-mode controlled DC motor drives under simple proportional control. In this paper, the phenomena of Hopf bifurcation and chaos from torus breakdown in a voltage-mode controlled DC drive system is reported. It has been shown that Hopf bifurcation may occur when the DC drive system adopts a more practical proportional-integral control. The phenomena of period-adding and phase-locking are also observed after the Hopf bifurcation. Furthermore, it is shown that the stable torus can breakdown and chaos emerges afterwards. The work presented in this paper provides more complete information about the dynamical behaviors of DC drive systems.

Stability and Hopf Bifurcation of Fractional-Order Complex-Valued Single Neuron Model with Time Delay

Science.gov (United States)

Wang, Zhen; Wang, Xiaohong; Li, Yuxia; Huang, Xia

2017-12-01

In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory of fractional-order differential equations and Laplace transforms, several new sufficient conditions, which ensure the stability of the system are derived. Taking the time delay as the bifurcation parameter, Hopf bifurcation is investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. Finally, two representative numerical examples are given to show the effectiveness of the theoretical results.

Delay Induced Hopf Bifurcation of an Epidemic Model with Graded Infection Rates for Internet Worms

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Tao Zhao

2017-01-01

Full Text Available A delayed SEIQRS worm propagation model with different infection rates for the exposed computers and the infectious computers is investigated in this paper. The results are given in terms of the local stability and Hopf bifurcation. Sufficient conditions for the local stability and the existence of Hopf bifurcation are obtained by using eigenvalue method and choosing the delay as the bifurcation parameter. In particular, the direction and the stability of the Hopf bifurcation are investigated by means of the normal form theory and center manifold theorem. Finally, a numerical example is also presented to support the obtained theoretical results.

DINÁMICA DE LA BIFURCACIÓN DE HOPF EN UNA CLASE DE MODELOS DE COMPETENCIA QUE EXHIBEN LA BIFURCACIÓN ZIP Hopf Bifurcation Dynamic in a Class of Competence Model Exhibiting Zip Bifurcation

Directory of Open Access Journals (Sweden)

Carlos Mario Escobar Callejas

2011-12-01

Full Text Available En el presente artículo de investigación se caracteriza el tipo de bifurcación de Hopf que se presenta en el fenómeno de la bifurcación de zip para un sistema tridimensional no lineal de ecuaciones diferenciales que satisface las condiciones planteadas por Butler y Farkas, las cuales modelan la competición de dos especies predadoras por una presa singular que se regenera. Se demuestra que en todas las variedades bidimensionales invariantes del sistema considerado se desarrolla una bifurcación de Hopf supercrítica lo cual es una extensión de algunos resultados sobre el tipo de bifurcación de Hopf que se forma en el fenómeno de la bifurcación de zip en sistema con respuesta funcional del predador del tipo Holling II, [1].This research article characterizes the type of Hopf bifurcation occurring in the Zip bifurcation phenomenon for a non-linear 3D system of differential equations which meets the conditions stated by Butler and Farkas to model competition of two predators struggling for a prey. It is shown that a supercritical Hopf bifurcation is developed in all invariant two-dimensional varieties of the system considered, which is an extension of some results about the kind of Hopf bifurcation which is formed in the Zip bifurcation phenomenon in a system with functional response of the Holling-type predator.

Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network

Directory of Open Access Journals (Sweden)

Zizhen Zhang

2013-01-01

Full Text Available A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.

Stability and Hopf Bifurcation in a Computer Virus Model with Multistate Antivirus

Directory of Open Access Journals (Sweden)

Tao Dong

2012-01-01

Full Text Available By considering that people may immunize their computers with countermeasures in susceptible state, exposed state and using anti-virus software may take a period of time, a computer virus model with time delay based on an SEIR model is proposed. We regard time delay as bifurcating parameter to study the dynamical behaviors which include local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when time delay passes through a sequence of critical value. The linerized model and stability of the bifurcating periodic solutions are also derived by applying the normal form theory and the center manifold theorem. Finally, an illustrative example is also given to support the theoretical results.

Hopf bifurcation in love dynamical models with nonlinear couples and time delays

International Nuclear Information System (INIS)

Liao Xiaofeng; Ran Jiouhong

2007-01-01

A love dynamical models with nonlinear couples and two delays is considered. Local stability of this model is studied by analyzing the associated characteristic transcendental equation. We find that the Hopf bifurcation occurs when the sum of the two delays varies and passes a sequence of critical values. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Numerical example is given to illustrate our results

The Boundary-Hopf-Fold Bifurcation in Filippov Systems

NARCIS (Netherlands)

Efstathiou, Konstantinos; Liu, Xia; Broer, Henk W.

2015-01-01

This paper studies the codimension-3 boundary-Hopf-fold (BHF) bifurcation of planar Filippov systems. Filippov systems consist of at least one discontinuity boundary locally separating the phase space to disjoint components with different dynamics. Such systems find applications in several fields,

Forced phase-locked response of a nonlinear system with time delay after Hopf bifurcation

International Nuclear Information System (INIS)

Ji, J.C.; Hansen, Colin H.

2005-01-01

The trivial equilibrium of a nonlinear autonomous system with time delay may become unstable via a Hopf bifurcation of multiplicity two, as the time delay reaches a critical value. This loss of stability of the equilibrium is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. The resultant dynamic behaviour of the corresponding nonlinear non-autonomous system in the neighbourhood of the Hopf bifurcation is investigated based on the reduction of the infinite-dimensional problem to a four-dimensional centre manifold. As a result of the interaction between the Hopf bifurcating periodic solutions and the external periodic excitation, a primary resonance can occur in the forced response of the system when the forcing frequency is close to the Hopf bifurcating periodic frequency. The method of multiple scales is used to obtain four first-order ordinary differential equations that determine the amplitudes and phases of the phase-locked periodic solutions. The first-order approximations of the periodic solutions are found to be in excellent agreement with those obtained by direct numerical integration of the delay-differential equation. It is also found that the steady state solutions of the nonlinear non-autonomous system may lose their stability via either a pitchfork or Hopf bifurcation. It is shown that the primary resonance response may exhibit symmetric and asymmetric phase-locked periodic motions, quasi-periodic motions, chaotic motions, and coexistence of two stable motions

Stability and Hopf bifurcation in a simplified BAM neural network with two time delays.

Science.gov (United States)

Cao, Jinde; Xiao, Min

2007-03-01

Various local periodic solutions may represent different classes of storage patterns or memory patterns, and arise from the different equilibrium points of neural networks (NNs) by applying Hopf bifurcation technique. In this paper, a bidirectional associative memory NN with four neurons and multiple delays is considered. By applying the normal form theory and the center manifold theorem, analysis of its linear stability and Hopf bifurcation is performed. An algorithm is worked out for determining the direction and stability of the bifurcated periodic solutions. Numerical simulation results supporting the theoretical analysis are also given.

Hopf bifurcation formula for first order differential-delay equations

Science.gov (United States)

Rand, Richard; Verdugo, Anael

2007-09-01

This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The derivation is accomplished using Lindstedt's perturbation method.

Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation

KAUST Repository

Abdelkefi, Abdessattar

2013-06-18

In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.

Views on the Hopf bifurcation with respect to voltage instabilities

Energy Technology Data Exchange (ETDEWEB)

Roa-Sepulveda, C A [Universidad de Concepcion, Concepcion (Chile). Dept. de Ingenieria Electrica; Knight, U G [Imperial Coll. of Science and Technology, London (United Kingdom). Dept. of Electrical and Electronic Engineering

1994-12-31

This paper presents a sensitivity study of the Hopf bifurcation phenomenon which can in theory appear in power systems, with reference to the dynamics of the process and the impact of demand characteristics. Conclusions are drawn regarding power levels at which these bifurcations could appear and concern the concept of the imaginary axis as a `hard` limit eigenvalue analyses. (author) 20 refs., 31 figs.

Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays

Directory of Open Access Journals (Sweden)

Huitao Zhao

2013-01-01

Full Text Available A ratio-dependent predator-prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. Using a global Hopf bifurcation result of Wu (1998 for functional differential equations, the global existence of the periodic solutions is obtained. Finally, an example for numerical simulations is also included.

Hopf and Bautin Bifurcation in a Tritrophic Food Chain Model with Holling Functional Response Types III and IV

Science.gov (United States)

Castellanos, Víctor; Castillo-Santos, Francisco Eduardo; Dela-Rosa, Miguel Angel; Loreto-Hernández, Iván

In this paper, we analyze the Hopf and Bautin bifurcation of a given system of differential equations, corresponding to a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. We distinguish two cases, when the prey has linear or logistic growth. In both cases we guarantee the existence of a limit cycle bifurcating from an equilibrium point in the positive octant of ℝ3. In order to do so, for the Hopf bifurcation we compute explicitly the first Lyapunov coefficient, the transversality Hopf condition, and for the Bautin bifurcation we also compute the second Lyapunov coefficient and verify the regularity conditions.

Stability and Hopf Bifurcation of a Reaction-Diffusion Neutral Neuron System with Time Delay

Science.gov (United States)

Dong, Tao; Xia, Linmao

2017-12-01

In this paper, a type of reaction-diffusion neutral neuron system with time delay under homogeneous Neumann boundary conditions is considered. By constructing a basis of phase space based on the eigenvectors of the corresponding Laplace operator, the characteristic equation of this system is obtained. Then, by selecting time delay and self-feedback strength as the bifurcating parameters respectively, the dynamic behaviors including local stability and Hopf bifurcation near the zero equilibrium point are investigated when the time delay and self-feedback strength vary. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by using the normal form and the center manifold theorem for the corresponding partial differential equation. Finally, two simulation examples are given to verify the theory.

Degenerate Hopf bifurcation in a self-exciting Faraday disc dynamo

Indian Academy of Sciences (India)

Weiquan Pan

2017-05-31

May 31, 2017 ... Recently, self-exciting Faraday disk dynamo is also a topic of con- cern [16–20]. ..... Hopf bifurcation. (a) Projected on the x–z plane and (b) pro- ... Key Lab of Com- plex System Optimization and Big Data Processing. (No.

Nonintegrability of the unfolding of the fold-Hopf bifurcation

Science.gov (United States)

Yagasaki, Kazuyuki

2018-02-01

We consider the unfolding of the codimension-two fold-Hopf bifurcation and prove its meromorphic nonintegrability in the meaning of Bogoyavlenskij for almost all parameter values. Our proof is based on a generalized version of the Morales-Ramis-Simó theory for non-Hamiltonian systems and related variational equations up to second order are used.

Si'lnikov chaos and Hopf bifurcation analysis of Rucklidge system

International Nuclear Information System (INIS)

Wang Xia

2009-01-01

A three-dimensional autonomous system - the Rucklidge system is considered. By the analytical method, Hopf bifurcation of Rucklidge system may occur when choosing an appropriate bifurcation parameter. Using the undetermined coefficient method, the existence of heteroclinic and homoclinic orbits in the Rucklidge system is proved, and the explicit and uniformly convergent algebraic expressions of Si'lnikov type orbits are given. As a result, the Si'lnikov criterion guarantees that there exists the Smale horseshoe chaos motion for the Rucklidge system.

Stability and Hopf bifurcation analysis of a new system

International Nuclear Information System (INIS)

Huang Kuifei; Yang Qigui

2009-01-01

In this paper, a new chaotic system is introduced. The system contains special cases as the modified Lorenz system and conjugate Chen system. Some subtle characteristics of stability and Hopf bifurcation of the new chaotic system are thoroughly investigated by rigorous mathematical analysis and symbolic computations. Meanwhile, some numerical simulations for justifying the theoretical analysis are also presented.

Hopf bifurcations in a fractional reaction–diffusion model for the ...

African Journals Online (AJOL)

The phenomenon of hopf bifurcation has been well-studied and applied to many physical situations to explain behaviour of solutions resulting from differential and partial differential equations. This phenomenon is applied to a fractional reaction diffusion model for tumor invasion and development. The result suggests that ...

A codimension two bifurcation in a railway bogie system

DEFF Research Database (Denmark)

Zhang, Tingting; True, Hans; Dai, Huanyun

2017-01-01

In this paper, a comprehensive analysis is presented to investigate a codimension two bifurcation that exists in a nonlinear railway bogie dynamic system combining theoretical analysis with numerical investigation. By using the running velocity V and the primary longitudinal stiffness (Formula...... coexist in a range of the bifurcation parameters which can lead to jumps in the lateral oscillation amplitude of the railway bogie system. Furthermore, reduce the values of the bifurcation parameters gradually. Firstly, the supercritical Hopf bifurcation turns into a subcritical one with multiple limit...

Stability and Hopf bifurcations in a competitive Lotka-Volterra system with two delays

International Nuclear Information System (INIS)

Song Yongli; Han Maoan; Peng Yahong

2004-01-01

We consider a Lotka-Volterra competition system with two delays. We first investigate the stability of the positive equilibrium and the existence of Hopf bifurcations, and then using the normal form theory and center manifold argument, derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions

Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System

Science.gov (United States)

Ma, Junhai; Ren, Wenbo

On the basis of our previous research, we deepen and complete a kind of macroeconomics IS-LM model with fractional-order calculus theory, which is a good reflection on the memory characteristics of economic variables, we also focus on the influence of the variables on the real system, and improve the analysis capabilities of the traditional economic models to suit the actual macroeconomic environment. The conditions of Hopf bifurcation in fractional-order system models are briefly demonstrated, and the fractional order when Hopf bifurcation occurs is calculated, showing the inherent complex dynamic characteristics of the system. With numerical simulation, bifurcation, strange attractor, limit cycle, waveform and other complex dynamic characteristics are given; and the order condition is obtained with respect to time. We find that the system order has an important influence on the running state of the system. The system has a periodic motion when the order meets the conditions of Hopf bifurcation; the fractional-order system gradually stabilizes with the change of the order and parameters while the corresponding integer-order system diverges. This study has certain significance to policy-making about macroeconomic regulation and control.

Stability of small-amplitude periodic solutions near Hopf bifurcations in time-delayed fully-connected PLL networks

Science.gov (United States)

Ferruzzo Correa, Diego P.; Bueno, Átila M.; Castilho Piqueira, José R.

2017-04-01

In this paper we investigate stability conditions for small-amplitude periodic solutions emerging near symmetry-preserving Hopf bifurcations in a time-delayed fully-connected N-node PLL network. The study of this type of systems which includes the time delay between connections has attracted much attention among researchers mainly because the delayed coupling between nodes emerges almost naturally in mathematical modeling in many areas of science such as neurobiology, population dynamics, physiology and engineering. In a previous work it has been shown that symmetry breaking and symmetry preserving Hopf bifurcations can emerge in the parameter space. We analyze the stability along branches of periodic solutions near fully-synchronized Hopf bifurcations in the fixed-point space, based on the reduction of the infinite-dimensional space onto a two-dimensional center manifold in normal form. Numerical results are also presented in order to confirm our analytical results.

Hopf bifurcation of a ratio-dependent predator-prey system with time delay

International Nuclear Information System (INIS)

Celik, Canan

2009-01-01

In this paper, we consider a ratio dependent predator-prey system with time delay where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the system based on the normal form approach and the center manifold theory. Finally, we illustrate our theoretical results by numerical simulations.

Hopf Bifurcation of a Delayed Epidemic Model with Information Variable and Limited Medical Resources

Directory of Open Access Journals (Sweden)

Caijuan Yan

2014-01-01

Full Text Available We consider SIR epidemic model in which population growth is subject to logistic growth in absence of disease. We get the condition for Hopf bifurcation of a delayed epidemic model with information variable and limited medical resources. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. If the basic reproduction ratio ℛ01, we obtain sufficient conditions under which the endemic equilibrium E* of system is locally asymptotically stable. And we also have discussed the stability and direction of Hopf bifurcations. Numerical simulations are carried out to explain the mathematical conclusions.

Stability and Hopf bifurcation in a delayed competitive web sites model

International Nuclear Information System (INIS)

Xiao Min; Cao Jinde

2006-01-01

The delayed differential equations modeling competitive web sites, based on the Lotka-Volterra competition equations, are considered. Firstly, the linear stability is investigated. It is found that there is a stability switch for time delay, and Hopf bifurcation occurs when time delay crosses through a critical value. Then the direction and stability of the bifurcated periodic solutions are determined, using the normal form theory and the center manifold reduction. Finally, some numerical simulations are carried out to illustrate the results found

Bifurcation analysis of a three dimensional system

Directory of Open Access Journals (Sweden)

Yongwen WANG

2018-04-01

Full Text Available In order to enrich the stability and bifurcation theory of the three dimensional chaotic systems, taking a quadratic truncate unfolding system with the triple singularity equilibrium as the research subject, the existence of the equilibrium, the stability and the bifurcation of the system near the equilibrium under different parametric conditions are studied. Using the method of mathematical analysis, the existence of the real roots of the corresponding characteristic equation under the different parametric conditions is analyzed, and the local manifolds of the equilibrium are gotten, then the possible bifurcations are guessed. The parametric conditions under which the equilibrium is saddle-focus are analyzed carefully by the Cardan formula. Moreover, the conditions of codimension-one Hopf bifucation and the prerequisites of the supercritical and subcritical Hopf bifurcation are found by computation. The results show that the system has abundant stability and bifurcation, and can also supply theorical support for the proof of the existence of the homoclinic or heteroclinic loop connecting saddle-focus and the Silnikov's chaos. This method can be extended to study the other higher nonlinear systems.

Hopf bifurcation and uncontrolled stochastic traffic-induced chaos in an RED-AQM congestion control system

International Nuclear Information System (INIS)

Wang Jun-Song; Yuan Rui-Xi; Gao Zhi-Wei; Wang De-Jin

2011-01-01

We study the Hopf bifurcation and the chaos phenomena in a random early detection-based active queue management (RED-AQM) congestion control system with a communication delay. We prove that there is a critical value of the communication delay for the stability of the RED-AQM control system. Furthermore, we show that the system will lose its stability and Hopf bifurcations will occur when the delay exceeds the critical value. When the delay is close to its critical value, we demonstrate that typical chaos patterns may be induced by the uncontrolled stochastic traffic in the RED-AQM control system even if the system is still stable, which reveals a new route to the chaos besides the bifurcation in the network congestion control system. Numerical simulations are given to illustrate the theoretical results. (general)

Competition of Spatial and Temporal Instabilities under Time Delay near Codimension-Two Turing-Hopf Bifurcations

International Nuclear Information System (INIS)

Wang Huijuan; Ren Zhi

2011-01-01

Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation. The time delay changes remarkably the oscillation frequency, the intrinsic wave vector, and the intensities of both Turing and Hopf modes. The application of appropriate time delay can control the competition between the Turing and Hopf modes. Analysis shows that individual or both feedbacks can realize the control of the transformation between the Turing and Hopf patterns. Two-dimensional numerical simulations validate the analytical results. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks.

Science.gov (United States)

Wang, Zhen; Campbell, Sue Ann

2017-11-01

We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with Z N symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.

Symmetry, Hopf bifurcation, and the emergence of cluster solutions in time delayed neural networks

Science.gov (United States)

Wang, Zhen; Campbell, Sue Ann

2017-11-01

We consider the networks of N identical oscillators with time delayed, global circulant coupling, modeled by a system of delay differential equations with ZN symmetry. We first study the existence of Hopf bifurcations induced by the coupling time delay and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of symmetric cluster oscillations. We apply our results to a case study: a network of FitzHugh-Nagumo neurons with diffusive coupling. For this model, we derive the asymptotic stability, global asymptotic stability, absolute instability, and stability switches of the equilibrium point in the plane of coupling time delay (τ) and excitability parameter (a). We investigate the patterns of cluster oscillations induced by the time delay and determine the direction and stability of the bifurcating periodic orbits by employing the multiple timescales method and normal form theory. We find that in the region where stability switching occurs, the dynamics of the system can be switched from the equilibrium point to any symmetric cluster oscillation, and back to equilibrium point as the time delay is increased.

Stability Switches, Hopf Bifurcations, and Spatio-temporal Patterns in a Delayed Neural Model with Bidirectional Coupling

Science.gov (United States)

Song, Yongli; Zhang, Tonghua; Tadé, Moses O.

2009-12-01

The dynamical behavior of a delayed neural network with bi-directional coupling is investigated by taking the delay as the bifurcating parameter. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. As the propagation time delay in the coupling varies, stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. We also discuss the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay differential equations combined with representation theory of Lie groups. In particular, we obtain that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling, i.e., different ranges of delays correspond to different patterns of neural activities. Numerical simulations are given to illustrate the obtained results and show the existence of bursts in some interval of the time for large enough delay.

Local and global Hopf bifurcation analysis in a neutral-type neuron system with two delays

Science.gov (United States)

Lv, Qiuyu; Liao, Xiaofeng

2018-03-01

In recent years, neutral-type differential-difference equations have been applied extensively in the field of engineering, and their dynamical behaviors are more complex than that of the delay differential-difference equations. In this paper, the equations used to describe a neutral-type neural network system of differential difference equation with two delays are studied (i.e. neutral-type differential equations). Firstly, by selecting τ1, τ2 respectively as a parameter, we provide an analysis about the local stability of the zero equilibrium point of the equations, and sufficient conditions of asymptotic stability for the system are derived. Secondly, by using the theory of normal form and applying the theorem of center manifold introduced by Hassard et al., the Hopf bifurcation is found and some formulas for deciding the stability of periodic solutions and the direction of Hopf bifurcation are given. Moreover, by applying the theorem of global Hopf bifurcation, the existence of global periodic solution of the system is studied. Finally, an example is given, and some computer numerical simulations are taken to demonstrate and certify the correctness of the presented results.

Hopf bifurcation in a partial dependent predator-prey system with delay

International Nuclear Information System (INIS)

Zhao Huitao; Lin Yiping

2009-01-01

In this paper, a partial dependent predator-prey model with time delay is studied by using the theory of functional differential equation and Hassard's method, the condition on which positive equilibrium exists and Hopf bifurcation occurs are given. Finally, numerical simulations are performed to support the analytical results, and the chaotic behaviors are observed.

Global Hopf bifurcation analysis on a BAM neural network with delays

Science.gov (United States)

Sun, Chengjun; Han, Maoan; Pang, Xiaoming

2007-01-01

A delayed differential equation that models a bidirectional associative memory (BAM) neural network with four neurons is considered. By using a global Hopf bifurcation theorem for FDE and a Bendixon's criterion for high-dimensional ODE, a group of sufficient conditions for the system to have multiple periodic solutions are obtained when the sum of delays is sufficiently large.

Global Hopf bifurcation analysis on a BAM neural network with delays

International Nuclear Information System (INIS)

Sun Chengjun; Han Maoan; Pang Xiaoming

2007-01-01

A delayed differential equation that models a bidirectional associative memory (BAM) neural network with four neurons is considered. By using a global Hopf bifurcation theorem for FDE and a Bendixon's criterion for high-dimensional ODE, a group of sufficient conditions for the system to have multiple periodic solutions are obtained when the sum of delays is sufficiently large

Hopf bifurcation of an (n + 1) -neuron bidirectional associative memory neural network model with delays.

Science.gov (United States)

Xiao, Min; Zheng, Wei Xing; Cao, Jinde

2013-01-01

Recent studies on Hopf bifurcations of neural networks with delays are confined to simplified neural network models consisting of only two, three, four, five, or six neurons. It is well known that neural networks are complex and large-scale nonlinear dynamical systems, so the dynamics of the delayed neural networks are very rich and complicated. Although discussing the dynamics of networks with a few neurons may help us to understand large-scale networks, there are inevitably some complicated problems that may be overlooked if simplified networks are carried over to large-scale networks. In this paper, a general delayed bidirectional associative memory neural network model with n + 1 neurons is considered. By analyzing the associated characteristic equation, the local stability of the trivial steady state is examined, and then the existence of the Hopf bifurcation at the trivial steady state is established. By applying the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction and stability of the bifurcating periodic solution. Furthermore, the paper highlights situations where the Hopf bifurcations are particularly critical, in the sense that the amplitude and the period of oscillations are very sensitive to errors due to tolerances in the implementation of neuron interconnections. It is shown that the sensitivity is crucially dependent on the delay and also significantly influenced by the feature of the number of neurons. Numerical simulations are carried out to illustrate the main results.

Hopf bifurcation of a free boundary problem modeling tumor growth with two time delays

International Nuclear Information System (INIS)

Xu Shihe

2009-01-01

In this paper, a free boundary problem modeling tumor growth with two discrete delays is studied. The delays respectively represents the time taken for cells to undergo mitosis and the time taken for the cell to modify the rate of cell loss due to apoptosis. We show the influence of time delays on the Hopf bifurcation when one of delays as a bifurcation parameter.

On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields

Directory of Open Access Journals (Sweden)

Michail P. Markakis

2016-01-01

Full Text Available The restriction of an n-dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. Normal forms regarding degenerate Hopf bifurcations up to codimension 3, as well as the corresponding Lyapunov coefficients and bifurcation portraits, can be easily computed for any system under consideration.

Hopf bifurcation and chaos in macroeconomic models with policy lag

International Nuclear Information System (INIS)

Liao Xiaofeng; Li Chuandong; Zhou Shangbo

2005-01-01

In this paper, we consider the macroeconomic models with policy lag, and study how lags in policy response affect the macroeconomic stability. The local stability of the nonzero equilibrium of this equation is investigated by analyzing the corresponding transcendental characteristic equation of its linearized equation. Some general stability criteria involving the policy lag and the system parameter are derived. By choosing the policy lag as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcation. The direction and stability of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Moreover, we show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system become locally unstable when the policy lag is too long. We also find the chaotic behavior in some range of the policy lag

Hopf bifurcation in a reaction-diffusive two-species model with nonlocal delay effect and general functional response

International Nuclear Information System (INIS)

Han, Renji; Dai, Binxiang

2017-01-01

Highlights: • We model general two-dimensional reaction-diffusion with nonlocal delay. • The existence of unique positive steady state is studied. • The bilinear form for the proposed system is given. • The existence, direction of Hopf bifurcation are given by symmetry method. - Abstract: A nonlocal delayed reaction-diffusive two-species model with Dirichlet boundary condition and general functional response is investigated in this paper. Based on the Lyapunov–Schmidt reduction, the existence, bifurcation direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady-state solution are obtained, where the time delay is taken as the bifurcation parameter. Moreover, the general results are applied to a diffusive Lotka–Volterra type food-limited population model with nonlocal delay effect, and it is found that diffusion and nonlocal delay can also affect the other dynamic behavior of the system by numerical experiments.

Delayed feedback on the dynamical model of a financial system

International Nuclear Information System (INIS)

Son, Woo-Sik; Park, Young-Jai

2011-01-01

Research highlights: → Effect of delayed feedbacks on the financial model. → Proof on the occurrence of Hopf bifurcation by local stability analysis. → Numerical bifurcation analysis on delay differential equations. → Observation of supercritical and subcritical Hopf, fold limit cycle, Neimark-Sacker, double Hopf and generalized Hopf bifurcations. - Abstract: We investigate the effect of delayed feedbacks on the financial model, which describes the time variation of the interest rate, the investment demand, and the price index, for establishing the fiscal policy. By local stability analysis, we theoretically prove the occurrences of Hopf bifurcation. Through numerical bifurcation analysis, we obtain the supercritical and subcritical Hopf bifurcation curves which support the theoretical predictions. Moreover, the fold limit cycle and Neimark-Sacker bifurcation curves are detected. We also confirm that the double Hopf and generalized Hopf codimension-2 bifurcation points exist.

Hopf Bifurcation Control of Subsynchronous Resonance Utilizing UPFC

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Μ. Μ. Alomari

2017-06-01

Full Text Available The use of a unified power flow controller (UPFC to control the bifurcations of a subsynchronous resonance (SSR in a multi-machine power system is introduced in this study. UPFC is one of the flexible AC transmission systems (FACTS where a voltage source converter (VSC is used based on gate-turn-off (GTO thyristor valve technology. Furthermore, UPFC can be used as a stabilizer by means of a power system stabilizer (PSS. The considered system is a modified version of the second system of the IEEE second benchmark model of subsynchronous resonance where the UPFC is added to its transmission line. The dynamic effects of the machine components on SSR are considered. Time domain simulations based on the complete nonlinear dynamical mathematical model are used for numerical simulations. The results in case of including UPFC are compared to the case where the transmission line is conventionally compensated (without UPFC where two Hopf bifurcations are predicted with unstable operating point at wide range of compensation levels. For UPFC systems, it is worth to mention that the operating point of the system never loses stability at all realistic compensation degrees and therefore all power system bifurcations have been eliminated.

Hopf bifurcation and eigenvalue sensitivity analysis of doubly fed induction generator wind turbine system

DEFF Research Database (Denmark)

Yang, Li Hui; Xu, Zhao; Østergaard, Jacob

2010-01-01

This paper first presents the Hopf bifurcation analysis for a vector-controlled doubly fed induction generator (DFIG) which is widely used in wind power conversion systems. Using three-phase back-to-back pulse-width-modulated (PWM) converters, DFIG can keep stator frequency constant under variabl...

Numerical Exploration of Kaldorian Macrodynamics: Hopf-Neimark Bifurcations and Business Cycles with Fixed Exchange Rates

Directory of Open Access Journals (Sweden)

Toichiro Asada

2007-01-01

Full Text Available We explore numerically a three-dimensional discrete-time Kaldorian macrodynamic model in an open economy with fixed exchange rates, focusing on the effects of variation of the model parameters, the speed of adjustment of the goods market α, and the degree of capital mobility β on the stability of equilibrium and on the existence of business cycles. We determine the stability region in the parameter space and find that increase of α destabilizes the equilibrium more quickly than increase of β. We determine the Hopf-Neimark bifurcation curve along which business cycles are generated, and discuss briefly the occurrence of Arnold tongues. Bifurcation and Lyapunov exponent diagrams are computed providing information on the emergence, persistence, and amplitude of the cycles and illustrating the complex dynamics involved. Examples of cycles and other attractors are presented. Finally, we discuss a two-dimensional variation of the model related to a “wealth effect,” called model 2, and show that in this case, α does not destabilize the equilibrium more quickly than β, and that a Hopf-Neimark bifurcation curve does not exist in the parameter space, therefore model 2 does not produce cycles.

Nonlinear stability, bifurcation and resonance in granular plane Couette flow

Science.gov (United States)

Shukla, Priyanka; Alam, Meheboob

2010-11-01

A weakly nonlinear stability theory is developed to understand the effect of nonlinearities on various linear instability modes as well as to unveil the underlying bifurcation scenario in a two-dimensional granular plane Couette flow. The relevant order parameter equation, the Landau-Stuart equation, for the most unstable two-dimensional disturbance has been derived using the amplitude expansion method of our previous work on the shear-banding instability.ootnotetextShukla and Alam, Phys. Rev. Lett. 103, 068001 (2009). Shukla and Alam, J. Fluid Mech. (2010, accepted). Two types of bifurcations, Hopf and pitchfork, that result from travelling and stationary linear instabilities, respectively, are analysed using the first Landau coefficient. It is shown that the subcritical instability can appear in the linearly stable regime. The present bifurcation theory shows that the flow is subcritically unstable to disturbances of long wave-lengths (kx˜0) in the dilute limit, and both the supercritical and subcritical states are possible at moderate densities for the dominant stationary and traveling instabilities for which kx=O(1). We show that the granular plane Couette flow is prone to a plethora of resonances.ootnotetextShukla and Alam, J. Fluid Mech. (submitted, 2010)

Hopf Bifurcation Analysis of a Gene Regulatory Network Mediated by Small Noncoding RNA with Time Delays and Diffusion

Science.gov (United States)

Li, Chengxian; Liu, Haihong; Zhang, Tonghua; Yan, Fang

2017-12-01

In this paper, a gene regulatory network mediated by small noncoding RNA involving two time delays and diffusion under the Neumann boundary conditions is studied. Choosing the sum of delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated by analyzing the corresponding characteristic equation. It is shown that the sum of delays can induce Hopf bifurcation and the diffusion incorporated into the system can effect the amplitude of periodic solutions. Furthermore, the spatially homogeneous periodic solution always exists and the spatially inhomogeneous periodic solution will arise when the diffusion coefficients of protein and mRNA are suitably small. Particularly, the small RNA diffusion coefficient is more robust and its effect on model is much less than protein and mRNA. Finally, the explicit formulae for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by employing the normal form theory and center manifold theorem for partial functional differential equations. Finally, numerical simulations are carried out to illustrate our theoretical analysis.

Noise-induced transitions at a Hopf bifurcation in a first-order delay-differential equation

International Nuclear Information System (INIS)

Longtin, A.

1991-01-01

The influence of colored noise on the Hopf bifurcation in a first-order delay-differential equation (DDE), a model paradigm for nonlinear delayed feedback systems, is considered. First, it is shown, using a stability analysis, how the properties of the DDE depend on the ratio R of system delay to response time. When this ratio is small, the DDE behaves more like a low-dimensional system of ordinary differential equations (ODE's); when R is large, one obtains a singular perturbation limit in which the behavior of the DDE approaches that of a discrete time map. The relative magnitude of the additive and multiplicative noise-induced postponements of the Hopf bifurcation are numerically shown to depend on the ratio R. Although both types of postponements are minute in the large-R limit, they are almost equal due to an equivalence of additive and parametric noise for discrete time maps. When R is small, the multiplicative shift is larger than the additive one at large correlation times, but the shifts are equal for small correlation times. In fact, at constant noise power, the postponement is only slightly affected by the correlation time of the noise, except when the noise becomes white, in which case the postponement drastically decreases. This is a numerical study of the stochastic Hopf bifurcation, in ODE's or DDE's, that looks at the effect of noise correlation time at constant power. Further, it is found that the slope at the fixed point averaged over the stochastic-parameter motion acts, under certain conditions, as a quantitative indicator of oscillation onset in the presence of noise. The problem of how properties of the DDE carry over to ODE's and to maps is discussed, along with the proper theoretical framework in which to study nonequilibrium phase transitions in this class of functional differential equations

Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model

DEFF Research Database (Denmark)

Brøns, Morten; Desroches, Mathieu; Krupa, Martin

2015-01-01

In a forest pest model, young trees are distinguished from old trees. The pest feeds on old trees. The pest grows on a fast scale, the young trees on an intermediate scale, and the old trees on a slow scale. A combination of a singular Hopf bifurcation and a “weak return” mechanism, characterized...

Homoclinic connections and subcritical Neimark bifurcation in a duopoly model with adaptively adjusted productions

International Nuclear Information System (INIS)

Agliari, Anna

2006-01-01

In this paper we study some global bifurcations arising in the Puu's oligopoly model when we assume that the producers do not adjust to the best reply but use an adaptive process to obtain at each step the new production. Such bifurcations cause the appearance of a pair of closed invariant curves, one attracting and one repelling, this latter being involved in the subcritical Neimark bifurcation of the Cournot equilibrium point. The aim of the paper is to highlight the relationship between the global bifurcations causing the appearance/disappearance of two invariant closed curves and the homoclinic connections of some saddle cycle, already conjectured in [Agliari A, Gardini L, Puu T. Some global bifurcations related to the appearance of closed invariant curves. Comput Math Simul 2005;68:201-19]. We refine the results obtained in such a paper, showing that the appearance/disappearance of closed invariant curves is not necessarily related to the existence of an attracting cycle. The characterization of the periodicity tongues (i.e. a region of the parameter space in which an attracting cycle exists) associated with a subcritical Neimark bifurcation is also discussed

Stability and Hopf bifurcation on a model for HIV infection of CD4{sup +} T cells with delay

Energy Technology Data Exchange (ETDEWEB)

Wang Xia [College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000 (China)], E-mail: xywangxia@163.com; Tao Youde [College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000 (China); Beijing Institute of Information Control, Beijing 100037 (China); Song Xinyu [College of Mathematics and Information Science, Xinyang Normal University, Xinyang, Henan 464000 (China) and Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091 (China)], E-mail: xysong88@163.com

2009-11-15

In this paper, a delayed differential equation model that describes HIV infection of CD4{sup +} T cells is considered. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. In succession, using the normal form theory and center manifold argument, we derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions.

Stability and dynamics of a controlled van der Pol-Duffing oscillator

International Nuclear Information System (INIS)

Ji, J.C.; Hansen, C.H.

2006-01-01

The trivial equilibrium of a van der Pol-Duffing oscillator under a linear-plus-nonlinear feedback control may change its stability either via a single or via a double Hopf bifurcation if the time delay involved in the feedback reaches certain values. It is found that the trivial equilibrium may lose its stability via a subcritical or supercritical Hopf bifurcation and regain its stability via a reverse subcritical or supercritical Hopf bifurcation as the time delay increases. A stable limit cycle appears after a supercritical Hopf bifurcation occurs and disappears through a reverse supercritical Hopf bifurcation. The interaction of the weakly periodic excitation and the stable bifurcating solution is investigated for the forced system under primary resonance conditions. It is shown that the forced periodic response may lose its stability via a Neimark-Sacker bifurcation. Analytical results are validated by a comparison with those of direct numerical integration

Nonlinear dynamics approach of modeling the bifurcation for aircraft wing flutter in transonic speed

DEFF Research Database (Denmark)

Matsushita, Hiroshi; Miyata, T.; Christiansen, Lasse Engbo

2002-01-01

The procedure of obtaining the two-degrees-of-freedom, finite dimensional. nonlinear mathematical model. which models the nonlinear features of aircraft flutter in transonic speed is reported. The model enables to explain every feature of the transonic flutter data of the wind tunnel tests...... conducted at National Aerospace Laboratory in Japan for a high aspect ratio wing. It explains the nonlinear features of the transonic flutter such as the subcritical Hopf bifurcation of a limit cycle oscillation (LCO), a saddle-node bifurcation, and an unstable limit cycle as well as a normal (linear...

Chaos and Hopf bifurcation of a hybrid ratio-dependent three species food chain

International Nuclear Information System (INIS)

Wang Fengyan; Pang Guoping

2008-01-01

In this paper, we propose and study a model of a hybrid ratio-dependent three species food chain, which is constituted by a hybrid type subsystem of prey and middle-predator and a middle-top predators' subsystem with Holling type-II functional response. We investigate the persistence and Hopf bifurcation of the system. Computer simulations are carried out to explain the mathematical conclusions. The chaotic attractor is obtained for suitable choice of parametric values

On control of Hopf bifurcation in time-delayed neural network system

International Nuclear Information System (INIS)

Zhou Shangbo; Liao Xiaofeng; Yu Juebang; Wong Kwokwo

2005-01-01

The control of Hopf bifurcations in neural network systems is studied in this Letter. The asymptotic stability theorem and the relevant corollary for linearized nonlinear dynamical systems are proven. In particular, a novel method for analyzing the local stability of a dynamical system with time-delay is suggested. For the time-delayed system consisting of one or two neurons, a washout filter based control model is proposed and analyzed. By employing the stability theorems derived, we investigate the stability of a control system and state the relevant theorems for choosing the parameters of the stabilized control system

Bifurcations and chaos in convection taking non-Fourier heat-flux

Science.gov (United States)

Layek, G. C.; Pati, N. C.

2017-11-01

In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.

Anticontrol of Hopf bifurcation and control of chaos for a finance system through washout filters with time delay.

Science.gov (United States)

Zhao, Huitao; Lu, Mengxia; Zuo, Junmei

2014-01-01

A controlled model for a financial system through washout-filter-aided dynamical feedback control laws is developed, the problem of anticontrol of Hopf bifurcation from the steady state is studied, and the existence, stability, and direction of bifurcated periodic solutions are discussed in detail. The obtained results show that the delay on price index has great influences on the financial system, which can be applied to suppress or avoid the chaos phenomenon appearing in the financial system.

Transverse single-file diffusion and enhanced longitudinal diffusion near a subcritical bifurcation

Science.gov (United States)

Dessup, Tommy; Coste, Christophe; Saint Jean, Michel

2018-05-01

A quasi-one-dimensional system of repelling particles undergoes a configurational phase transition when the transverse confining potential decreases. Below a threshold, it becomes energetically favorable for the system to adopt one of two staggered raw patterns, symmetric with respect to the system axis. This transition is a subcritical pitchfork bifurcation for short range interactions. As a consequence, the homogeneous zigzag pattern is unstable in a finite zigzag amplitude range [hC 1,hC 2] . We exhibit strong qualitative effects of the subcriticality on the thermal motions of the particles. When the zigzag amplitude is close enough to the limits hC 1 and hC 2, a transverse vibrational soft mode occurs which induces a strongly subdiffusive behavior of the transverse fluctuations, similar to single-file diffusion. On the contrary, the longitudinal fluctuations are enhanced, with a diffusion coefficient which is more than doubled. Conversely, a simple measurement of the thermal fluctuations allows a precise determination of the bifurcation thresholds.

Stability switches, Hopf bifurcation and chaos of a neuron model with delay-dependent parameters

International Nuclear Information System (INIS)

Xu, X.; Hu, H.Y.; Wang, H.L.

2006-01-01

It is very common that neural network systems usually involve time delays since the transmission of information between neurons is not instantaneous. Because memory intensity of the biological neuron usually depends on time history, some of the parameters may be delay dependent. Yet, little attention has been paid to the dynamics of such systems. In this Letter, a detailed analysis on the stability switches, Hopf bifurcation and chaos of a neuron model with delay-dependent parameters is given. Moreover, the direction and the stability of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem. It shows that the dynamics of the neuron model with delay-dependent parameters is quite different from that of systems with delay-independent parameters only

Travelling waves and their bifurcations in the Lorenz-96 model

Science.gov (United States)

van Kekem, Dirk L.; Sterk, Alef E.

2018-03-01

In this paper we study the dynamics of the monoscale Lorenz-96 model using both analytical and numerical means. The bifurcations for positive forcing parameter F are investigated. The main analytical result is the existence of Hopf or Hopf-Hopf bifurcations in any dimension n ≥ 4. Exploiting the circulant structure of the Jacobian matrix enables us to reduce the first Lyapunov coefficient to an explicit formula from which it can be determined when the Hopf bifurcation is sub- or supercritical. The first Hopf bifurcation for F > 0 is always supercritical and the periodic orbit born at this bifurcation has the physical interpretation of a travelling wave. Furthermore, by unfolding the codimension two Hopf-Hopf bifurcation it is shown to act as an organising centre, explaining dynamics such as quasi-periodic attractors and multistability, which are observed in the original Lorenz-96 model. Finally, the region of parameter values beyond the first Hopf bifurcation value is investigated numerically and routes to chaos are described using bifurcation diagrams and Lyapunov exponents. The observed routes to chaos are various but without clear pattern as n → ∞.

A heterogenous Cournot duopoly with delay dynamics: Hopf bifurcations and stability switching curves

Science.gov (United States)

Pecora, Nicolò; Sodini, Mauro

2018-05-01

This article considers a Cournot duopoly model in a continuous-time framework and analyze its dynamic behavior when the competitors are heterogeneous in determining their output decision. Specifically the model is expressed in the form of differential equations with discrete delays. The stability conditions of the unique Nash equilibrium of the system are determined and the emergence of Hopf bifurcations is shown. Applying some recent mathematical techniques (stability switching curves) and performing numerical simulations, the paper confirms how different time delays affect the stability of the economy.

Non linear stability analysis of parallel channels with natural circulation

Energy Technology Data Exchange (ETDEWEB)

Mishra, Ashish Mani; Singh, Suneet, E-mail: suneet.singh@iitb.ac.in

2016-12-01

Highlights: • Nonlinear instabilities in natural circulation loop are studied. • Generalized Hopf points, Sub and Supercritical Hopf bifurcations are identified. • Bogdanov–Taken Point (BT Point) is observed by nonlinear stability analysis. • Effect of parameters on stability of system is studied. - Abstract: Linear stability analysis of two-phase flow in natural circulation loop is quite extensively studied by many researchers in past few years. It can be noted that linear stability analysis is limited to the small perturbations only. It is pointed out that such systems typically undergo Hopf bifurcation. If the Hopf bifurcation is subcritical, then for relatively large perturbation, the system has unstable limit cycles in the (linearly) stable region in the parameter space. Hence, linear stability analysis capturing only infinitesimally small perturbations is not sufficient. In this paper, bifurcation analysis is carried out to capture the non-linear instability of the dynamical system and both subcritical and supercritical bifurcations are observed. The regions in the parameter space for which subcritical and supercritical bifurcations exist are identified. These regions are verified by numerical simulation of the time-dependent, nonlinear ODEs for the selected points in the operating parameter space using MATLAB ODE solver.

Complexity dynamics and Hopf bifurcation analysis based on the first Lyapunov coefficient about 3D IS-LM macroeconomics system

Science.gov (United States)

Ma, Junhai; Ren, Wenbo; Zhan, Xueli

2017-04-01

Based on the study of scholars at home and abroad, this paper improves the three-dimensional IS-LM model in macroeconomics, analyzes the equilibrium point of the system and stability conditions, focuses on the parameters and complex dynamic characteristics when Hopf bifurcation occurs in the three-dimensional IS-LM macroeconomics system. In order to analyze the stability of limit cycles when Hopf bifurcation occurs, this paper further introduces the first Lyapunov coefficient to judge the limit cycles, i.e. from a practical view of the business cycle. Numerical simulation results show that within the range of most of the parameters, the limit cycle of 3D IS-LM macroeconomics is stable, that is, the business cycle is stable; with the increase of the parameters, limit cycles becomes unstable, and the value range of the parameters in this situation is small. The research results of this paper have good guide significance for the analysis of macroeconomics system.

Stability and Hopf bifurcation in a delayed model for HIV infection of CD4{sup +}T cells

Energy Technology Data Exchange (ETDEWEB)

Cai Liming [Department of Mathematics, Xinyang Normal University, Xinyang, 464000 Henan (China); Beijing Institute of Information Control, Beijing 100037 (China)], E-mail: lmcai06@yahoo.com.cn; Li Xuezhi [Department of Mathematics, Xinyang Normal University, Xinyang, 464000 Henan (China)

2009-10-15

In this paper, we consider a delayed mathematical model for the interactions of HIV infection and CD4{sup +}T cells. We first investigate the existence and stability of the Equilibria. We then study the effect of the time delay on the stability of the infected equilibrium. Criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. Moreover, by applying Nyquist criterion, the length of delay is estimated for which stability continues to hold. Finally by using a delay {tau} as a bifurcation parameter, the existence of Hopf bifurcation is also investigated. Numerical simulations are presented to illustrate the analytical results.

Effects of time delays on stability and Hopf bifurcation in a fractional ring-structured network with arbitrary neurons

Science.gov (United States)

Huang, Chengdai; Cao, Jinde; Xiao, Min; Alsaedi, Ahmed; Hayat, Tasawar

2018-04-01

This paper is comprehensively concerned with the dynamics of a class of high-dimension fractional ring-structured neural networks with multiple time delays. Based on the associated characteristic equation, the sum of time delays is regarded as the bifurcation parameter, and some explicit conditions for describing delay-dependent stability and emergence of Hopf bifurcation of such networks are derived. It reveals that the stability and bifurcation heavily relies on the sum of time delays for the proposed networks, and the stability performance of such networks can be markedly improved by selecting carefully the sum of time delays. Moreover, it is further displayed that both the order and the number of neurons can extremely influence the stability and bifurcation of such networks. The obtained criteria enormously generalize and improve the existing work. Finally, numerical examples are presented to verify the efficiency of the theoretical results.

Discretization analysis of bifurcation based nonlinear amplifiers

Science.gov (United States)

Feldkord, Sven; Reit, Marco; Mathis, Wolfgang

2017-09-01

Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.

Bifurcation analysis of the simplified models of boiling water reactor and identification of global stability boundary

Energy Technology Data Exchange (ETDEWEB)

Pandey, Vikas; Singh, Suneet, E-mail: suneet.singh@iitb.ac.in

2017-04-15

Highlights: • Non-linear stability analysis of nuclear reactor is carried out. • Global and local stability boundaries are drawn in the parameter space. • Globally stable, bi-stable, and unstable regions have been demarcated. • The identification of the regions is verified by numerical simulations. - Abstract: Nonlinear stability study of the neutron coupled thermal hydraulics instability has been carried out by several researchers for boiling water reactors (BWRs). The focus of these studies has been to identify subcritical and supercritical Hopf bifurcations. Supercritical Hopf bifurcation are soft or safe due to the fact that stable limit cycles arise in linearly unstable region; linear and global stability boundaries are same for this bifurcation. It is well known that the subcritical bifurcations can be considered as hard or dangerous due to the fact that unstable limit cycles (nonlinear phenomena) exist in the (linearly) stable region. The linear stability leads to a stable equilibrium in such regions, only for infinitesimally small perturbations. However, finite perturbations lead to instability due to the presence of unstable limit cycles. Therefore, it is evident that the linear stability analysis is not sufficient to understand the exact stability characteristics of BWRs. However, the effect of these bifurcations on the stability boundaries has been rarely discussed. In the present work, the identification of global stability boundary is demonstrated using simplified models. Here, five different models with different thermal hydraulics feedback have been investigated. In comparison to the earlier works, current models also include the impact of adding the rate of change in temperature on void reactivity as well as effect of void reactivity on rate of change of temperature. Using the bifurcation analysis of these models the globally stable region in the parameter space has been identified. The globally stable region has only stable solutions and

Bifurcation analysis of the simplified models of boiling water reactor and identification of global stability boundary

International Nuclear Information System (INIS)

Pandey, Vikas; Singh, Suneet

2017-01-01

Highlights: • Non-linear stability analysis of nuclear reactor is carried out. • Global and local stability boundaries are drawn in the parameter space. • Globally stable, bi-stable, and unstable regions have been demarcated. • The identification of the regions is verified by numerical simulations. - Abstract: Nonlinear stability study of the neutron coupled thermal hydraulics instability has been carried out by several researchers for boiling water reactors (BWRs). The focus of these studies has been to identify subcritical and supercritical Hopf bifurcations. Supercritical Hopf bifurcation are soft or safe due to the fact that stable limit cycles arise in linearly unstable region; linear and global stability boundaries are same for this bifurcation. It is well known that the subcritical bifurcations can be considered as hard or dangerous due to the fact that unstable limit cycles (nonlinear phenomena) exist in the (linearly) stable region. The linear stability leads to a stable equilibrium in such regions, only for infinitesimally small perturbations. However, finite perturbations lead to instability due to the presence of unstable limit cycles. Therefore, it is evident that the linear stability analysis is not sufficient to understand the exact stability characteristics of BWRs. However, the effect of these bifurcations on the stability boundaries has been rarely discussed. In the present work, the identification of global stability boundary is demonstrated using simplified models. Here, five different models with different thermal hydraulics feedback have been investigated. In comparison to the earlier works, current models also include the impact of adding the rate of change in temperature on void reactivity as well as effect of void reactivity on rate of change of temperature. Using the bifurcation analysis of these models the globally stable region in the parameter space has been identified. The globally stable region has only stable solutions and

Effect of Carreau-Yasuda rheological parameters on subcritical Lapwood convection in horizontal porous cavity saturated by shear-thinning fluid

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Khechiba, Khaled; Mamou, Mahmoud; Hachemi, Madjid; Delenda, Nassim; Rebhi, Redha

2017-06-01

The present study is focused on Lapwood convection in isotropic porous media saturated with non-Newtonian shear thinning fluid. The non-Newtonian rheological behavior of the fluid is modeled using the general viscosity model of Carreau-Yasuda. The convection configuration consists of a shallow porous cavity with a finite aspect ratio and subject to a vertical constant heat flux, whereas the vertical walls are maintained impermeable and adiabatic. An approximate analytical solution is developed on the basis of the parallel flow assumption, and numerical solutions are obtained by solving the full governing equations. The Darcy model with the Boussinesq approximation and energy transport equations are solved numerically using a finite difference method. The results are obtained in terms of the Nusselt number and the flow fields as functions of the governing parameters. A good agreement is obtained between the analytical approximation and the numerical solution of the full governing equations. The effects of the rheological parameters of the Carreau-Yasuda fluid and Rayleigh number on the onset of subcritical convection thresholds are demonstrated. Regardless of the aspect ratio of the enclosure and thermal boundary condition type, the subcritical convective flows are seen to occur below the onset of stationary convection. Correlations are proposed to estimate the subcritical Rayleigh number for the onset of finite amplitude convection as a function of the fluid rheological parameters. Linear stability of the convective motion, predicted by the parallel flow approximation, is studied, and the onset of Hopf bifurcation, from steady convective flow to oscillatory behavior, is found to depend strongly on the rheological parameters. In general, Hopf bifurcation is triggered earlier as the fluid becomes more and more shear-thinning.

Nonlinear analysis of a closed-loop tractor-semitrailer vehicle system with time delay

Science.gov (United States)

Liu, Zhaoheng; Hu, Kun; Chung, Kwok-wai

2016-08-01

In this paper, a nonlinear analysis is performed on a closed-loop system of articulated heavy vehicles with driver steering control. The nonlinearity arises from the nonlinear cubic tire force model. An integration method is employed to derive an analytical periodic solution of the system in the neighbourhood of the critical speed. The results show that excellent accuracy can be achieved for the calculation of periodic solutions arising from Hopf bifurcation of the vehicle motion. A criterion is obtained for detecting the Bautin bifurcation which separates branches of supercritical and subcritical Hopf bifurcations. The integration method is compared to the incremental harmonic balance method in both supercritical and subcritical scenarios.

Stability and bifurcation of a discrete BAM neural network model with delays

International Nuclear Information System (INIS)

Zheng Baodong; Zhang Yang; Zhang Chunrui

2008-01-01

A map modelling a discrete bidirectional associative memory neural network with delays is investigated. Its dynamics is studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Numerical simulation is performed to verify the analytical results

Bifurcation Analysis and Spatiotemporal Patterns in Unidirectionally Delay-Coupled Vibratory Gyroscopes

Science.gov (United States)

Li, Li; Xu, Jian

Time delay is inevitable in unidirectionally coupled drive-free vibratory gyroscope system. The effect of time delay on the gyroscope system is studied in this paper. To this end, amplitude death and Hopf bifurcation induced by small time delay are first investigated by analyzing the related characteristic equation. Then, the direction of Hopf bifurcations and stability of Hopf-bifurcating periodic oscillations are determined by calculating the normal form on the center manifold. Next, spatiotemporal patterns of these Hopf-bifurcating periodic oscillations are analyzed by using the symmetric bifurcation theory of delay differential equations. Finally, it is found that numerical simulations agree with the associated analytic results. These phenomena could be induced although time delay is very small. Therefore, it is shown that time delay is an important factor which influences the sensitivity and accuracy of the gyroscope system and cannot be neglected during the design and manufacture.

On period doubling bifurcations of cycles and the harmonic balance method

International Nuclear Information System (INIS)

Itovich, Griselda R.; Moiola, Jorge L.

2006-01-01

This works attempts to give quasi-analytical expressions for subharmonic solutions appearing in the vicinity of a Hopf bifurcation. Starting with well-known tools as the graphical Hopf method for recovering the periodic branch emerging from classical Hopf bifurcation, precise frequency and amplitude estimations of the limit cycle can be obtained. These results allow to attain approximations for period doubling orbits by means of harmonic balance techniques, whose accuracy is established by comparison of Floquet multipliers with continuation software packages. Setting up a few coefficients, the proposed methodology yields to approximate solutions that result from a second period doubling bifurcation of cycles and to extend the validity limits of the graphical Hopf method

Onset of Fast Magnetic Reconnection via Subcritical Bifurcation

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ZHIBIN eGUO

2015-04-01

Full Text Available We report a phase transition model for the onset of fast magnetic reconnection. By investigating the joint dynamics of streaming instability(i.e., current driven ion acoustic in this paper and current gradient driven whistler wave {color{blue} {prior to the onset of fast reconnection}}, we show that the nonlinear evolution of current sheet(CS can be described by a Landau-Ginzburg equation. The phase transition from slow reconnection to fast reconnection occurs at a critical thickness, $Delta_csimeq frac{2}{sqrt{pi}}left|frac{v_{the}}{v_c}right|d_e$, where $v_{the}$ is electron thermal velocity and $v_c$ is the velocity threshold of the streaming instability. For current driven ion acoustic, $Delta_c$ is $leq10d_e$. If the thickness of the CS is narrower than $Delta_c$, the CS subcritically bifurcates into a rough state, which facilitates breakage of the CS, and consequently initiates fast reconnection.

Stability and bifurcation analysis in a delayed SIR model

International Nuclear Information System (INIS)

Jiang Zhichao; Wei Junjie

2008-01-01

In this paper, a time-delayed SIR model with a nonlinear incidence rate is considered. The existence of Hopf bifurcations at the endemic equilibrium is established by analyzing the distribution of the characteristic values. A explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. Numerical simulations to support the analytical conclusions are carried out

Singular Hopf bifurcation in a differential equation with large state-dependent delay.

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Kozyreff, G; Erneux, T

2014-02-08

We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawtooth oscillations. The dependence of the delay on the solution can be either linear or nonlinear, with at least quadratic dependence. In the former case, an asymptotic connection is made with the Rayleigh oscillator. In the latter, van der Pol's equation is derived for the small-amplitude oscillations. SDD differential equations are currently the subject of intense research in order to establish or amend general theorems valid for constant-delay differential equation, but explicit analytical construction of solutions are rare. This paper illustrates the use of singular perturbation techniques and the unusual way in which solvability conditions can arise for SDD problems with large delays.

Identification of dynamic basins in boiling fluxes

International Nuclear Information System (INIS)

Juanico, L.E.

1997-01-01

A theoretical and experimental study of the dynamic behavior of a boiling channel is presented. In particular, the existence of different basins of attraction during instabilities was established. A fully analytical treatment of boiling channel dynamics were performed using a algebraic delay model. Subcritical and supercritical Hopf bifurcations could be identified and analyzed using perturbation methods. The derivation of a fully analytical criterion for Hopf bifurcation transcription was applied to determine the amplitude of the limit cycles and the maximum allowed perturbations necessary to break the system stability. A lumped parameters model which allows the representation of flow reversal is presented. The dynamic of very large amplitude oscillations, out of the Hopf bifurcation domain, was studied. The analysis revealed the existence of new dynamical basins of attraction, where the system may evolve to and return from with hysteresis. Finally, an experimental study was conducted, in a water loop at atmospheric pressure, designed to reproduce the operating conditions analyzed in the theory. Different dynamic phase previously predicted in the theory were found and their nonlinear characteristics were studied. In particular, subcritical and supercritical Hopf bifurcations and very large amplitude oscillations with flow reversal were identified. (author). 53 refs., figs

Bifurcation analysis on a generalized recurrent neural network with two interconnected three-neuron components

International Nuclear Information System (INIS)

Hajihosseini, Amirhossein; Maleki, Farzaneh; Rokni Lamooki, Gholam Reza

2011-01-01

Highlights: → We construct a recurrent neural network by generalizing a specific n-neuron network. → Several codimension 1 and 2 bifurcations take place in the newly constructed network. → The newly constructed network has higher capabilities to learn periodic signals. → The normal form theorem is applied to investigate dynamics of the network. → A series of bifurcation diagrams is given to support theoretical results. - Abstract: A class of recurrent neural networks is constructed by generalizing a specific class of n-neuron networks. It is shown that the newly constructed network experiences generic pitchfork and Hopf codimension one bifurcations. It is also proved that the emergence of generic Bogdanov-Takens, pitchfork-Hopf and Hopf-Hopf codimension two, and the degenerate Bogdanov-Takens bifurcation points in the parameter space is possible due to the intersections of codimension one bifurcation curves. The occurrence of bifurcations of higher codimensions significantly increases the capability of the newly constructed recurrent neural network to learn broader families of periodic signals.

Bifurcation theory for finitely smooth planar autonomous differential systems

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Han, Maoan; Sheng, Lijuan; Zhang, Xiang

2018-03-01

In this paper we establish bifurcation theory of limit cycles for planar Ck smooth autonomous differential systems, with k ∈ N. The key point is to study the smoothness of bifurcation functions which are basic and important tool on the study of Hopf bifurcation at a fine focus or a center, and of Poincaré bifurcation in a period annulus. We especially study the smoothness of the first order Melnikov function in degenerate Hopf bifurcation at an elementary center. As we know, the smoothness problem was solved for analytic and C∞ differential systems, but it was not tackled for finitely smooth differential systems. Here, we present their optimal regularity of these bifurcation functions and their asymptotic expressions in the finite smooth case.

Bifurcation Analysis of the QI 3-D Four-Wing Chaotic System

International Nuclear Information System (INIS)

Sun, Y.; Qi, G.; Wang, Z.; Wyk, B.J. van

2010-01-01

This paper analyzes the pitchfork and Hopf bifurcations of a new 3-D four-wing quadratic autonomous system proposed by Qi et al. The center manifold technique is used to reduce the dimensions of this system. The pitchfork and Hopf bifurcations of the system are theoretically analyzed. The influence of system parameters on other bifurcations are also investigated. The theoretical analysis and simulations demonstrate the rich dynamics of the system. (authors)

Hypercrater Bifurcations, Attractor Coexistence, and Unfolding in a 5D Model of Economic Dynamics

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Toichiro Asada

2011-01-01

Full Text Available Complex dynamical features are explored in a discrete interregional macrodynamic model proposed by Asada et al., using numerical methods. The model is five-dimensional with four parameters. The results demonstrate patterns of dynamical behaviour, such as bifurcation processes and coexistence of attractors, generated by high-dimensional discrete systems. In three cases of two-dimensional parameter subspaces the stability of equilibrium region is determined and its boundaries, the flip and Neimark-Hopf bifurcation curves, are identified by means of necessary coefficient criteria. In the first case closed invariant curves (CICs are found to occur through 5D-crater-type bifurcations, and for certain ranges of parameter values a stable equilibrium coexists with an unstable CIC associated with the subcritical bifurcation, as well as with an outer stable CIC. A remarkable feature of the second case is the coexistence of two attracting CICs outside the stability region. In both these cases the related hysteresis effects are illustrated by numerical simulations. In the third case a remarkable feature is the apparent unfolding of an attracting CIC before it evolves to a chaotic attractor. Examples of CICs and chaotic attractors are given in subspaces of phase space.

Bifurcation analysis and stability design for aircraft longitudinal motion with high angle of attack

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Xin Qi

2015-02-01

Full Text Available Bifurcation analysis and stability design for aircraft longitudinal motion are investigated when the nonlinearity in flight dynamics takes place severely at high angle of attack regime. To predict the special nonlinear flight phenomena, bifurcation theory and continuation method are employed to systematically analyze the nonlinear motions. With the refinement of the flight dynamics for F-8 Crusader longitudinal motion, a framework is derived to identify the stationary bifurcation and dynamic bifurcation for high-dimensional system. Case study shows that the F-8 longitudinal motion undergoes saddle node bifurcation, Hopf bifurcation, Zero-Hopf bifurcation and branch point bifurcation under certain conditions. Moreover, the Hopf bifurcation renders series of multiple frequency pitch oscillation phenomena, which deteriorate the flight control stability severely. To relieve the adverse effects of these phenomena, a stabilization control based on gain scheduling and polynomial fitting for F-8 longitudinal motion is presented to enlarge the flight envelope. Simulation results validate the effectiveness of the proposed scheme.

Stability and bifurcation of numerical discretization of a second-order delay differential equation with negative feedback

International Nuclear Information System (INIS)

Ding Xiaohua; Su Huan; Liu Mingzhu

2008-01-01

The paper analyzes a discrete second-order, nonlinear delay differential equation with negative feedback. The characteristic equation of linear stability is solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The existence of local Hopf bifurcations is investigated, and the direction and stability of periodic solutions bifurcating from the Hopf bifurcation of the discrete model are determined by the Hopf bifurcation theory of discrete system. Finally, some numerical simulations are performed to illustrate the analytical results found

O(2) Hopf bifurcation of viscous shock waves in a channel

Science.gov (United States)

Pogan, Alin; Yao, Jinghua; Zumbrun, Kevin

2015-07-01

Extending work of Texier and Zumbrun in the semilinear non-reflection symmetric case, we study O(2) transverse Hopf bifurcation, or "cellular instability", of viscous shock waves in a channel, for a class of quasilinear hyperbolic-parabolic systems including the equations of thermoviscoelasticity. The main difficulties are to (i) obtain Fréchet differentiability of the time- T solution operator by appropriate hyperbolic-parabolic energy estimates, and (ii) handle O(2) symmetry in the absence of either center manifold reduction (due to lack of spectral gap) or (due to nonstandard quasilinear hyperbolic-parabolic form) the requisite framework for treatment by spatial dynamics on the space of time-periodic functions, the two standard treatments for this problem. The latter issue is resolved by Lyapunov-Schmidt reduction of the time- T map, yielding a four-dimensional problem with O(2) plus approximate S1 symmetry, which we treat "by hand" using direct Implicit Function Theorem arguments. The former is treated by balancing information obtained in Lagrangian coordinates with that from associated constraints. Interestingly, this argument does not apply to gas dynamics or magnetohydrodynamics (MHD), due to the infinite-dimensional family of Lagrangian symmetries corresponding to invariance under arbitrary volume-preserving diffeomorphisms.

Effects of internal noise in mesoscopic chemical systems near Hopf bifurcation

International Nuclear Information System (INIS)

Xiao Tiejun; Ma Juan; Hou Zhonghuai; Xin Houwen

2007-01-01

The effects of internal noise in mesoscopic chemical oscillation systems have been studied analytically, in the parameter region close to the deterministic Hopf bifurcation. Starting from chemical Langevin equations, stochastic normal form equations are obtained, governing the evolution of the radius and phase of the stochastic oscillation. By stochastic averaging, the normal form equation can be solved analytically. Stationary distributions of the radius and auto-correlation functions of the phase variable are obtained. It is shown that internal noise can induce oscillation; even no deterministic oscillation exists. The radius of the noise-induced oscillation (NIO) becomes larger when the internal noise increases, but the correlation time becomes shorter. The trade-off between the strength and regularity of the NIO leads to a clear maximum in its signal-to-noise ratio when the internal noise changes, demonstrating the occurrence of internal noise coherent resonance. Since the intensity of the internal noise is inversely proportional to the system size, the phenomenon also indicates the existence of an optimal system size. These theoretical results are applied to a circadian clock system and excellent agreement with the numerical results is obtained

Two-phase flow instability and bifurcation analysis of inclined multiple uniformly heated channels - 15107

International Nuclear Information System (INIS)

Mishra, A.M.; Paul, S.; Singh, S.; Panday, V.

2015-01-01

In this paper the two-phase flow instability analysis of multiple heated channels with various inclinations is studied. In addition, the bifurcation analysis is also carried out to capture the nonlinear dynamics of the system and to identify the regions in parameter space for which subcritical and supercritical bifurcations exist. In order to carry out the analysis, the system is mathematically represented by nonlinear Partial Differential Equation (PDE) for mass, momentum and energy in single as well as two-phase region. Then converted into Ordinary Differential Equation (ODE) using weighted residual method. Also, coupling equation is being used under the assumption that pressure drop in each channel is the same and the total mass flow rate is equal to sum of the individual mass flow rates. The homogeneous equilibrium model is used for the analysis. Stability Map is obtained in terms of phase change number (Npch) and Subcooling Number (Nsb) by solving a set of nonlinear, coupled algebraic equations obtained at equilibrium using Newton Raphson Method. MATLAB Code is verified by comparing it with results obtained by Matcont (Open source software) under same parametric values. Numerical simulations of the time-dependent, nonlinear ODEs are carried out for selected points in the operating parameter space to obtain the actual damped and growing oscillations in the channel inlet flow velocity which confirms the stability region across the stability map. Generalized Hopf (GH) points are observed for different inclinations, they are also points for subcritical and supercritical bifurcations. (authors)

Stability and Hopf bifurcation for a business cycle model with expectation and delay

Science.gov (United States)

Liu, Xiangdong; Cai, Wenli; Lu, Jiajun; Wang, Yangyang

2015-08-01

According to rational expectation hypothesis, the government will take into account the future capital stock in the process of investment decision. By introducing anticipated capital stock into an economic model with investment delay, we construct a mixed functional differential system including delay and advanced variables. The system is converted to the one containing only delay by variable substitution. The equilibrium point of the system is obtained and its dynamical characteristics such as stability, Hopf bifurcation and its stability and direction are investigated by using the related theories of nonlinear dynamics. We carry out some numerical simulations to confirm these theoretical conclusions. The results indicate that both capital stock's anticipation and investment lag are the certain factors leading to the occurrence of cyclical fluctuations in the macroeconomic system. Moreover, the level of economic fluctuation can be dampened to some extent if investment decisions are made by the reasonable short-term forecast on capital stock.

Codimension-two bifurcation analysis on firing activities in Chay neuron model

International Nuclear Information System (INIS)

Duan Lixia; Lu Qishao

2006-01-01

Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing

Codimension-two bifurcation analysis on firing activities in Chay neuron model

Energy Technology Data Exchange (ETDEWEB)

Duan Lixia [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China); Lu Qishao [School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China)]. E-mail: qishaolu@hotmail.com

2006-12-15

Using codimension-two bifurcation analysis in the Chay neuron model, the relationship between the electric activities and the parameters of neurons is revealed. The whole parameter space is divided into two parts, that is, the firing and silence regions of neurons. It is found that the transition sets between firing and silence regions are composed of the Hopf bifurcation curves of equilibrium states and the saddle-node bifurcation curves of limit cycles, with some codimension-two bifurcation points. The transitions from silence to firing in neurons are due to the Hopf bifurcation or the fold limit cycle bifurcation, but the codimension-two singularities lead to complexity in dynamical behaviour of neuronal firing.

Iterative methods for the detection of Hopf bifurcations in finite element discretisation of incompressible flow problems

International Nuclear Information System (INIS)

Cliffe, K.A.; Garratt, T.J.; Spence, A.

1992-03-01

This paper is concerned with the problem of computing a small number of eigenvalues of large sparse generalised eigenvalue problems arising from mixed finite element discretisations of time dependent equations modelling viscous incompressible flow. The eigenvalues of importance are those with smallest real part and can be used in a scheme to determine the stability of steady state solutions and to detect Hopf bifurcations. We introduce a modified Cayley transform of the generalised eigenvalue problem which overcomes a drawback of the usual Cayley transform applied to such problems. Standard iterative methods are then applied to the transformed eigenvalue problem to compute approximations to the eigenvalue of smallest real part. Numerical experiments are performed using a model of double diffusive convection. (author)

Codimension-2 bifurcations of the Kaldor model of business cycle

International Nuclear Information System (INIS)

Wu, Xiaoqin P.

2011-01-01

Research highlights: → The conditions are given such that the characteristic equation may have purely imaginary roots and double zero roots. → Purely imaginary roots lead us to study Hopf and Bautin bifurcations and to calculate the first and second Lyapunov coefficients. → Double zero roots lead us to study Bogdanov-Takens (BT) bifurcation. → Bifurcation diagrams for Bautin and BT bifurcations are obtained by using the normal form theory. - Abstract: In this paper, complete analysis is presented to study codimension-2 bifurcations for the nonlinear Kaldor model of business cycle. Sufficient conditions are given for the model to demonstrate Bautin and Bogdanov-Takens (BT) bifurcations. By computing the first and second Lyapunov coefficients and performing nonlinear transformation, the normal forms are derived to obtain the bifurcation diagrams such as Hopf, homoclinic and double limit cycle bifurcations. Some examples are given to confirm the theoretical results.

Bifurcation of cubic nonlinear parallel plate-type structure in axial flow

International Nuclear Information System (INIS)

Lu Li; Yang Yiren

2005-01-01

The Hopf bifurcation of plate-type beams with cubic nonlinear stiffness in axial flow was studied. By assuming that all the plates have the same deflections at any instant, the nonlinear model of plate-type beam in axial flow was established. The partial differential equation was turned into an ordinary differential equation by using Galerkin method. A new algebraic criterion of Hopf bifurcation was utilized to in our analysis. The results show that there's no Hopf bifurcation for simply supported plate-type beams while the cantilevered plate-type beams has. At last, the analytic expression of critical flow velocity of cantilevered plate-type beams in axial flow and the purely imaginary eigenvalues of the corresponding linear system were gotten. (authors)

Bifurcation Analysis for an SEIRS-V Model with Delays on the Transmission of Worms in a Wireless Sensor Network

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Zizhen Zhang

2017-01-01

Full Text Available Hopf bifurcation for an SEIRS-V model with delays on the transmission of worms in a wireless sensor network is investigated. We focus on existence of the Hopf bifurcation by regarding the diverse delay as a bifurcation parameter. The results show that propagation of worms in the wireless sensor network can be controlled when the delay is suitably small under some certain conditions. Then, we study properties of the Hopf bifurcation by using the normal form theory and center manifold theorem. Finally, we give a numerical example to support the theoretical results.

Generalized Ginzburg-Landau equation for self-pulsing instability in a two-photon laser

Energy Technology Data Exchange (ETDEWEB)

Cunzheng, Ning; Haken, H [Inst. fuer Theoretische Physik und Synergetik, Univ. Stuttgart (Germany)

1989-10-01

A nonlinear analysis is made for a degenerate two-photon ring laser near its critical point corresponding to a self-pulsing instability by using the slaving principle and normal form theory. It turns out that the system undergoes two kinds of transitions, a usual Hopf bifurcation to a stable or unstable limit cycle and a co-dimension two Hopf bifurcation where the limit cycles disappear. An analytical criterion is given to distinguish the super - form the sub-critical bifurcation. We have also solved the equations numerically to confirm and to supplement our analytical results. In the case of super-critical bifurcation, a period-doubling bifurcation sequence to chaos is also observed with the decrease in pumping. (orig.).

Numerical results on noise-induced dynamics in the subthreshold regime for thermoacoustic systems

Science.gov (United States)

Gupta, Vikrant; Saurabh, Aditya; Paschereit, Christian Oliver; Kabiraj, Lipika

2017-03-01

Thermoacoustic instability is a serious issue in practical combustion systems. Such systems are inherently noisy, and hence the influence of noise on the dynamics of thermoacoustic instability is an aspect of practical importance. The present work is motivated by a recent report on the experimental observation of coherence resonance, or noise-induced coherence with a resonance-like dependence on the noise intensity as the system approaches the stability margin, for a prototypical premixed laminar flame combustor (Kabiraj et al., Phys. Rev. E, 4 (2015)). We numerically investigate representative thermoacoustic models for such noise-induced dynamics. Similar to the experiments, we study variation in system dynamics in response to variations in the noise intensity and in a critical control parameter as the systems approach their stability margins. The qualitative match identified between experimental results and observations in the representative models investigated here confirms that coherence resonance is a feature of thermoacoustic systems. We also extend the experimental results, which were limited to the case of subcritical Hopf bifurcation, to the case of supercritical Hopf bifurcation. We identify that the phenomenon has qualitative differences for the systems undergoing transition via subcritical and supercritical Hopf bifurcations. Two important practical implications are associated with the findings. Firstly, the increase in noise-induced coherence as the system approaches the onset of thermoacoustic instability can be considered as a precursor to the instability. Secondly, the dependence of noise-induced dynamics on the bifurcation type can be utilised to distinguish between subcritical and supercritical bifurcation prior to the onset of the instability.

Stability and bifurcation analysis in a kind of business cycle model with delay

International Nuclear Information System (INIS)

Zhang Chunrui; Wei Junjie

2004-01-01

A kind of business cycle model with delay is considered. Firstly, the linear stability of the model is studied and bifurcation set is drawn in the appropriate parameter plane. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Then the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived, using the normal form method and center manifold theorem. Finally, a group conditions to guarantee the global existence of periodic solutions is given, and numerical simulations are performed to illustrate the analytical results found

Bifurcation and Control in a Singular Phytoplankton-Zooplankton-Fish Model with Nonlinear Fish Harvesting and Taxation

Science.gov (United States)

Meng, Xin-You; Wu, Yu-Qian

In this paper, a delayed differential algebraic phytoplankton-zooplankton-fish model with taxation and nonlinear fish harvesting is proposed. In the absence of time delay, the existence of singularity induced bifurcation is discussed by regarding economic interest as bifurcation parameter. A state feedback controller is designed to eliminate singularity induced bifurcation. Based on Liu’s criterion, Hopf bifurcation occurs at the interior equilibrium when taxation is taken as bifurcation parameter and is more than its corresponding critical value. In the presence of time delay, by analyzing the associated characteristic transcendental equation, the interior equilibrium loses local stability when time delay crosses its critical value. What’s more, the direction of Hopf bifurcation and stability of the bifurcating periodic solutions are investigated based on normal form theory and center manifold theorem, and nonlinear state feedback controller is designed to eliminate Hopf bifurcation. Furthermore, Pontryagin’s maximum principle has been used to obtain optimal tax policy to maximize the benefit as well as the conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical analysis.

Bifurcations of Tumor-Immune Competition Systems with Delay

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Ping Bi

2014-01-01

Full Text Available A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability of the bifurcated periodic solutions are given for codimension one and codimension two bifurcations, including Hopf bifurcation, steady-state bifurcation, and B-T bifurcation. Numerical examples and simulations are given to illustrate the bifurcations analysis and obtained results.

An approach to normal forms of Kuramoto model with distributed delays and the effect of minimal delay

Energy Technology Data Exchange (ETDEWEB)

Niu, Ben, E-mail: niubenhit@163.com [Department of Mathematics, Harbin Institute of Technology, Weihai 264209 (China); Guo, Yuxiao [Department of Mathematics, Harbin Institute of Technology, Weihai 264209 (China); Jiang, Weihua [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China)

2015-09-25

Heterogeneous delays with positive lower bound (gap) are taken into consideration in Kuramoto model. On the Ott–Antonsen's manifold, the dynamical transitional behavior from incoherence to coherence is mediated by Hopf bifurcation. We establish a perturbation technique on complex domain, by which universal normal forms, stability and criticality of the Hopf bifurcation are obtained. Theoretically, a hysteresis loop is found near the subcritically bifurcated coherent state. With respect to Gamma distributed delay with fixed mean and variance, we find that the large gap decreases Hopf bifurcation value, induces supercritical bifurcations, avoids the hysteresis loop and significantly increases in the number of coexisting coherent states. The effect of gap is finally interpreted from the viewpoint of excess kurtosis of Gamma distribution. - Highlights: • Heterogeneously delay-coupled Kuramoto model with minimal delay is considered. • Perturbation technique on complex domain is established for bifurcation analysis. • Hysteresis phenomenon is investigated in a theoretical way. • The effect of excess kurtosis of distributed delays is discussed.

Bifurcation structure of a model of bursting pancreatic cells

DEFF Research Database (Denmark)

Mosekilde, Erik; Lading, B.; Yanchuk, S.

2001-01-01

. The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n + 1)-spike bursting...... behavior is born, slightly overlapping with a subcritical period-doubling bifurcation in which n-spike bursting behavior loses its stability.......One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other...

Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate

Science.gov (United States)

Ren, Jingli; Yuan, Qigang

2017-08-01

A three dimensional microbial continuous culture model with a restrained microbial growth rate is studied in this paper. Two types of dilution rates are considered to investigate the dynamic behaviors of the model. For the unforced system, fold bifurcation and Hopf bifurcation are detected, and numerical simulations reveal that the system undergoes degenerate Hopf bifurcation. When the system is periodically forced, bifurcation diagrams for periodic solutions of period-one and period-two are given by researching the Poincaré map, corresponding to different bifurcation cases in the unforced system. Stable and unstable quasiperiodic solutions are obtained by Neimark-Sacker bifurcation with different parameter values. Periodic solutions of various periods can occur or disappear and even change their stability, when the Poincaré map of the forced system undergoes Neimark-Sacker bifurcation, flip bifurcation, and fold bifurcation. Chaotic attractors generated by a cascade of period doublings and some phase portraits are given at last.

Identification of neural firing patterns, frequency and temporal coding mechanisms in individual aortic baroreceptors

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Huaguang eGu

2015-08-01

Full Text Available In rabbit depressor nerve fibers, an on-off firing pattern, period-1 firing, and integer multiple firing with quiescent state were observed as the static pressure level was increased. A bursting pattern with bursts at the systolic phase of blood pressure, continuous firing, and bursting with burst at diastolic phase and quiescent state at systolic phase were observed as the mean level of the dynamic blood pressure was increased. For both static and dynamic pressures, the firing frequency of the first two firing patterns increased and of the last firing pattern decreased due to the quiescent state. If the quiescent state is disregarded, the spike frequency becomes an increasing trend. The instantaneous spike frequency of the systolic phase bursting, continuous firing, and diastolic phase bursting can reflect the temporal process of the systolic phase, whole procedure, and diastolic phase of the dynamic blood pressure signal, respectively. With increasing the static current corresponding to pressure level, the deterministic Hodgkin-Huxley (HH model manifests a process from a resting state first to period-1 firing via a subcritical Hopf bifurcation and then to a resting state via a supercritical Hopf bifurcation, and the firing frequency increases. The on-off firing and integer multiple firing were here identified as noise-induced firing patterns near the subcritical and supercritical Hopf bifurcation points, respectively, using the stochastic HH model. The systolic phase bursting and diastolic phase bursting were identified as pressure-induced firings near the subcritical and supercritical Hopf bifurcation points, respectively, using an HH model with a dynamic signal. The firing, spike frequency, and instantaneous spike frequency observed in the experiment were simulated and explained using HH models. The results illustrate the dynamics of different firing patterns and the frequency and temporal coding mechanisms of aortic baroreceptor.

Bifurcation analysis in delayed feedback Jerk systems and application of chaotic control

International Nuclear Information System (INIS)

Zheng Baodong; Zheng Huifeng

2009-01-01

Jerk systems with delayed feedback are considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associated characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, the stability and direction of the Hopf bifurcation are determined by applying the normal form method and center manifold theorem. Finally, the application to chaotic control is investigated, and some numerical simulations are carried out to illustrate the obtained results.

Stability and bifurcation in a simplified four-neuron BAM neural network with multiple delays

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available We first study the distribution of the zeros of a fourth-degree exponential polynomial. Then we apply the obtained results to a simplified bidirectional associated memory (BAM neural network with four neurons and multiple time delays. By taking the sum of the delays as the bifurcation parameter, it is shown that under certain assumptions the steady state is absolutely stable. Under another set of conditions, there are some critical values of the delay, when the delay crosses these critical values, the Hopf bifurcation occurs. Furthermore, some explicit formulae determining the stability and the direction of periodic solutions bifurcating from Hopf bifurcations are obtained by applying the normal form theory and center manifold reduction. Numerical simulations supporting the theoretical analysis are also included.

Dynamics of a BWR with inclusion of boiling nonlinearity, clad temperature and void-dependent core power removal: Stability and bifurcation characteristics of advanced heavy water reactor (AHWR)

Energy Technology Data Exchange (ETDEWEB)

Verma, Dinkar, E-mail: dinkar@iitk.ac.in [Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016 (India); Kalra, Manjeet Singh, E-mail: drmanjeet.singh@dituniversity.edu.in [DIT University, Dehradun 248 009 (India); Wahi, Pankaj, E-mail: wahi@iitk.ac.in [Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016 (India)

2016-11-15

Highlights: • Simplified models with inclusion of the clad temperature are considered. • Boiling nonlinearity and core power removal have been modeled. • Method of multiple time scales has been used for nonlinear analysis to get the nature and amplitude of oscillations. • Incorporation of modeling complexities enhances the stability of system. • We find that reactors with higher nominal power are more desirable from the point of view of global stability. - Abstract: We study the effect of including boiling nonlinearity, clad temperature and void-dependent power removal from the primary loop in the mathematical modeling of a boiling water reactor (BWR) on its dynamic characteristics. The advanced heavy water reactor (AHWR) is taken as a case study. Towards this end, we have analyzed two different simplified models with different handling of the clad temperature. Each of these models has the necessary modifications pertaining to boiling nonlinearity and power removal from the primary loop. These simplified models incorporate the neutronics and thermal–hydraulic coupling. The effect of successive changes in the modeling assumptions on the linear stability of the reactor has been studied and we find that incorporation of each of these complexities in the model increases the stable operating region of the reactor. Further, the method of multiple time scales (MMTS) is exploited to carry out the nonlinear analysis with a view to predict the bifurcation characteristics of the reactor. Both subcritical and supercritical Hopf bifurcations are present in each model depending on the choice of operating parameters. These analytical observations from MMTS have been verified against numerical simulations. A parametric study on the effect of changing the nominal reactor power on the regions in the parametric space of void coefficient of reactivity and fuel temperature coefficient of reactivity with sub- and super-critical Hopf bifurcations has been performed for all

Stochastic stability and bifurcation in a macroeconomic model

International Nuclear Information System (INIS)

Li Wei; Xu Wei; Zhao Junfeng; Jin Yanfei

2007-01-01

On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis

Stability and Bifurcation Analysis of a Modified Epidemic Model for Computer Viruses

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Chuandong Li

2014-01-01

Full Text Available We extend the three-dimensional SIR model to four-dimensional case and then analyze its dynamical behavior including stability and bifurcation. It is shown that the new model makes a significant improvement to the epidemic model for computer viruses, which is more reasonable than the most existing SIR models. Furthermore, we investigate the stability of the possible equilibrium point and the existence of the Hopf bifurcation with respect to the delay. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. An analytical condition for determining the direction, stability, and other properties of bifurcating periodic solutions is obtained by using the normal form theory and center manifold argument. The obtained results may provide a theoretical foundation to understand the spread of computer viruses and then to minimize virus risks.

Bifurcation in the Lengyel–Epstein system for the coupled reactors with diffusion

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Shaban Aly

2016-01-01

Full Text Available The main goal of this paper is to continue the investigations of the important system of Fengqi et al. (2008. The occurrence of Turing and Hopf bifurcations in small homogeneous arrays of two coupled reactors via diffusion-linked mass transfer which described by a system of ordinary differential equations is considered. I study the conditions of the existence as well as stability properties of the equilibrium solutions and derive the precise conditions on the parameters to show that the Hopf bifurcation occurs. Analytically I show that a diffusion driven instability occurs at a certain critical value, when the system undergoes a Turing bifurcation, patterns emerge. The spatially homogeneous equilibrium loses its stability and two new spatially non-constant stable equilibria emerge which are asymptotically stable. Numerically, at a certain critical value of diffusion the periodic solution gets destabilized and two new spatially nonconstant periodic solutions arise by Turing bifurcation.

Hysteretic and intermittent regimes in the subcritical bifurcation of a quasi-one-dimensional system of interacting particles

Science.gov (United States)

Dessup, Tommy; Coste, Christophe; Saint Jean, Michel

2016-01-01

In this article, we study the effects of white Gaussian additive thermal noise on a subcritical pitchfork bifurcation. We consider a quasi-one-dimensional system of particles that are transversally confined, with short-range (non-Coulombic) interactions and periodic boundary conditions in the longitudinal direction. In such systems, there is a structural transition from a linear order to a staggered row, called the zigzag transition. There is a finite range of transverse confinement stiffnesses for which the stable configuration at zero temperature is a localized zigzag pattern surrounded by aligned particles, which evidences the subcriticality of the bifurcation. We show that these configurations remain stable for a wide temperature range. At zero temperature, the transition between a straight line and such localized zigzag patterns is hysteretic. We have studied the influence of thermal noise on the hysteresis loop. Its description is more difficult than at T =0 K since thermally activated jumps between the two configurations always occur and the system cannot stay forever in a unique metastable state. Two different regimes have to be considered according to the temperature value with respect to a critical temperature Tc(τobs) that depends on the observation time τobs. An hysteresis loop is still observed at low temperature, with a width that decreases as the temperature increases toward Tc(τobs) . In contrast, for T >Tc(τobs) the memory of the initial condition is lost by stochastic jumps between the configurations. The study of the mean residence times in each configuration gives a unique opportunity to precisely determine the barrier height that separates the two configurations, without knowing the complete energy landscape of this many-body system. We also show how to reconstruct the hysteresis loop that would exist at T =0 K from high-temperature simulations.

An upper limit for slow-earthquake zones: self-oscillatory behavior through the Hopf bifurcation mechanism from a spring-block model under lubricated surfaces

Science.gov (United States)

Castellanos-Rodríguez, Valentina; Campos-Cantón, Eric; Barboza-Gudiño, Rafael; Femat, Ricardo

2017-08-01

The complex oscillatory behavior of a spring-block model is analyzed via the Hopf bifurcation mechanism. The mathematical spring-block model includes Dieterich-Ruina's friction law and Stribeck's effect. The existence of self-sustained oscillations in the transition zone - where slow earthquakes are generated within the frictionally unstable region - is determined. An upper limit for this region is proposed as a function of seismic parameters and frictional coefficients which are concerned with presence of fluids in the system. The importance of the characteristic length scale L, the implications of fluids, and the effects of external perturbations in the complex dynamic oscillatory behavior, as well as in the stationary solution, are take into consideration.

Bifurcation of the spin-wave equations

International Nuclear Information System (INIS)

Cascon, A.; Koiller, J.; Rezende, S.M.

1990-01-01

We study the bifurcations of the spin-wave equations that describe the parametric pumping of collective modes in magnetic media. Mechanisms describing the following dynamical phenomena are proposed: (i) sequential excitation of modes via zero eigenvalue bifurcations; (ii) Hopf bifurcations followed (or not) by Feingenbaum cascades of period doubling; (iii) local and global homoclinic phenomena. Two new organizing center for routes to chaos are identified; in the classification given by Guckenheimer and Holmes [GH], one is a codimension-two local bifurcation, with one pair of imaginary eigenvalues and a zero eigenvalue, to which many dynamical consequences are known; secondly, global homoclinic bifurcations associated to splitting of separatrices, in the limit where the system can be considered a Hamiltonian subjected to weak dissipation and forcing. We outline what further numerical and algebraic work is necessary for the detailed study following this program. (author)

Bifurcation Control of an Electrostatically-Actuated MEMS Actuator with Time-Delay Feedback

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Lei Li

2016-10-01

Full Text Available The parametric excitation system consisting of a flexible beam and shuttle mass widely exists in microelectromechanical systems (MEMS, which can exhibit rich nonlinear dynamic behaviors. This article aims to theoretically investigate the nonlinear jumping phenomena and bifurcation conditions of a class of electrostatically-driven MEMS actuators with a time-delay feedback controller. Considering the comb structure consisting of a flexible beam and shuttle mass, the partial differential governing equation is obtained with both the linear and cubic nonlinear parametric excitation. Then, the method of multiple scales is introduced to obtain a slow flow that is analyzed for stability and bifurcation. Results show that time-delay feedback can improve resonance frequency and stability of the system. What is more, through a detailed mathematical analysis, the discriminant of Hopf bifurcation is theoretically derived, and appropriate time-delay feedback force can make the branch from the Hopf bifurcation point stable under any driving voltage value. Meanwhile, through global bifurcation analysis and saddle node bifurcation analysis, theoretical expressions about the system parameter space and maximum amplitude of monostable vibration are deduced. It is found that the disappearance of the global bifurcation point means the emergence of monostable vibration. Finally, detailed numerical results confirm the analytical prediction.

Bifurcation analysis and spatio-temporal patterns of nonlinear oscillations in a delayed neural network with unidirectional coupling

International Nuclear Information System (INIS)

Song Yongli; Tadé, Moses O; Zhang Tonghua

2009-01-01

In this paper, a delayed neural network with unidirectional coupling is considered which consists of two two-dimensional nonlinear differential equation systems with exponential decay where one system receives a delayed input from the other system. Some parameter regions are given for conditional/absolute stability and Hopf bifurcations by using the theory of functional differential equations. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the centre manifold theorem. We also investigate the spatio-temporal patterns of bifurcating periodic oscillations by using the symmetric bifurcation theory of delay-differential equations combined with representation theory of Lie groups. Then the global continuation of phase-locked periodic solutions is investigated. Numerical simulations are given to illustrate the results obtained

Convection in a nematic liquid crystal with homeotropic alignment and heated from below

Energy Technology Data Exchange (ETDEWEB)

Ahlers, G. [Univ. of California, Santa Barbara, CA (United States)

1995-12-31

Experimental results for convection in a thin horizontal layer of a homeotropically aligned nematic liquid crystal heated from below and in a vertical magnetic field are presented. A subcritical Hopf bifurcation leads to the convecting state. There is quantitative agreement between the measured and the predicted bifurcation line as a function of magnetic field. The nonlinear state near the bifurcation is one of spatio-temporal chaos which seems to be the result of a zig-zag instability of the straight-roll state.

Bifurcation and Stability in a Delayed Predator-Prey Model with Mixed Functional Responses

Science.gov (United States)

Yafia, R.; Aziz-Alaoui, M. A.; Merdan, H.; Tewa, J. J.

2015-06-01

The model analyzed in this paper is based on the model set forth by Aziz Alaoui et al. [Aziz Alaoui & Daher Okiye, 2003; Nindjin et al., 2006] with time delay, which describes the competition between the predator and prey. This model incorporates a modified version of the Leslie-Gower functional response as well as that of Beddington-DeAngelis. In this paper, we consider the model with one delay consisting of a unique nontrivial equilibrium E* and three others which are trivial. Their dynamics are studied in terms of local and global stabilities and of the description of Hopf bifurcation at E*. At the third trivial equilibrium, the existence of the Hopf bifurcation is proven as the delay (taken as a parameter of bifurcation) that crosses some critical values.

Bifurcation routes and economic stability

Czech Academy of Sciences Publication Activity Database

Vošvrda, Miloslav

2001-01-01

Roč. 8, č. 14 (2001), s. 43-59 ISSN 1212-074X R&D Projects: GA ČR GA402/00/0439; GA ČR GA402/01/0034; GA ČR GA402/01/0539 Institutional research plan: AV0Z1075907 Keywords : macroeconomic stability * foreign investment phenomenon * the Hopf bifurcation Subject RIV: AH - Economics

Analytical determination of the bifurcation thresholds in stochastic differential equations with delayed feedback.

Science.gov (United States)

Gaudreault, Mathieu; Drolet, François; Viñals, Jorge

2010-11-01

Analytical expressions for pitchfork and Hopf bifurcation thresholds are given for a nonlinear stochastic differential delay equation with feedback. Our results assume that the delay time τ is small compared to other characteristic time scales, not a significant limitation close to the bifurcation line. A pitchfork bifurcation line is found, the location of which depends on the conditional average , where x(t) is the dynamical variable. This conditional probability incorporates the combined effect of fluctuation correlations and delayed feedback. We also find a Hopf bifurcation line which is obtained by a multiple scale expansion around the oscillatory solution near threshold. We solve the Fokker-Planck equation associated with the slowly varying amplitudes and use it to determine the threshold location. In both cases, the predicted bifurcation lines are in excellent agreement with a direct numerical integration of the governing equations. Contrary to the known case involving no delayed feedback, we show that the stochastic bifurcation lines are shifted relative to the deterministic limit and hence that the interaction between fluctuation correlations and delay affect the stability of the solutions of the model equation studied.

Multistability and gluing bifurcation to butterflies in coupled networks with non-monotonic feedback

International Nuclear Information System (INIS)

Ma Jianfu; Wu Jianhong

2009-01-01

Neural networks with a non-monotonic activation function have been proposed to increase their capacity for memory storage and retrieval, but there is still a lack of rigorous mathematical analysis and detailed discussions of the impact of time lag. Here we consider a two-neuron recurrent network. We first show how supercritical pitchfork bifurcations and a saddle-node bifurcation lead to the coexistence of multiple stable equilibria (multistability) in the instantaneous updating network. We then study the effect of time delay on the local stability of these equilibria and show that four equilibria lose their stability at a certain critical value of time delay, and Hopf bifurcations of these equilibria occur simultaneously, leading to multiple coexisting periodic orbits. We apply centre manifold theory and normal form theory to determine the direction of these Hopf bifurcations and the stability of bifurcated periodic orbits. Numerical simulations show very interesting global patterns of periodic solutions as the time delay is varied. In particular, we observe that these four periodic solutions are glued together along the stable and unstable manifolds of saddle points to develop a butterfly structure through a complicated process of gluing bifurcations of periodic solutions

Stability and Bifurcation of a Computer Virus Propagation Model with Delay and Incomplete Antivirus Ability

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Jianguo Ren

2014-01-01

Full Text Available A new computer virus propagation model with delay and incomplete antivirus ability is formulated and its global dynamics is analyzed. The existence and stability of the equilibria are investigated by resorting to the threshold value R0. By analysis, it is found that the model may undergo a Hopf bifurcation induced by the delay. Correspondingly, the critical value of the Hopf bifurcation is obtained. Using Lyapunov functional approach, it is proved that, under suitable conditions, the unique virus-free equilibrium is globally asymptotically stable if R01. Numerical examples are presented to illustrate possible behavioral scenarios of the mode.

Bifurcations of a class of singular biological economic models

International Nuclear Information System (INIS)

Zhang Xue; Zhang Qingling; Zhang Yue

2009-01-01

This paper studies systematically a prey-predator singular biological economic model with time delay. It shows that this model exhibits two bifurcation phenomena when the economic profit is zero. One is transcritical bifurcation which changes the stability of the system, and the other is singular induced bifurcation which indicates that zero economic profit brings impulse, i.e., rapid expansion of the population in biological explanation. On the other hand, if the economic profit is positive, at a critical value of bifurcation parameter, the system undergoes a Hopf bifurcation, i.e., the increase of delay destabilizes the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results obtained here. In addition, we study numerically that the system undergoes a saddle-node bifurcation when the bifurcation parameter goes through critical value of positive economic profit.

On the analysis of local bifurcation and topological horseshoe of a new 4D hyper-chaotic system

International Nuclear Information System (INIS)

Zhou, Leilei; Chen, Zengqiang; Wang, Zhonglin; Wang, Jiezhi

2016-01-01

Highlights: • A new 4D smooth quadratic autonomous system with complex hyper-chaotic dynamics is presented. • The stability of equilibria is observed near the bifurcation points. • The Hopf bifurcation and pitchfork bifurcation are analyzed by using the center manifold theorem and bifurcation theory. • A horseshoe with two-directional expansions in the 4D hyper-chaotic system has been found, which rigorously proves the existence of hyper-chaos in theory. - Abstract: In this paper, a new four-dimensional (4D) smooth quadratic autonomous system with complex hyper-chaotic dynamics is presented and analyzed. The Lyapunov exponent (LE) spectrum, bifurcation diagram and various phase portraits of the system are provided. The stability, Hopf bifurcation and pitchfork bifurcation of equilibrium point are discussed by using the center manifold theorem and bifurcation theory. Numerical simulation results are consistent with the theoretical analysis. Besides, by combining the topological horseshoe theory with a computer-assisted method of Poincaré maps and utilizing the algorithm for finding horseshoes in 3D hyper-chaotic maps, a horseshoe with two-directional expansions in the 4D hyper-chaotic system is successfully found, which rigorously proves the existence of hyper-chaos in theory.

Bifurcation Behavior Analysis in a Predator-Prey Model

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Nan Wang

2016-01-01

Full Text Available A predator-prey model is studied mathematically and numerically. The aim is to explore how some key factors influence dynamic evolutionary mechanism of steady conversion and bifurcation behavior in predator-prey model. The theoretical works have been pursuing the investigation of the existence and stability of the equilibria, as well as the occurrence of bifurcation behaviors (transcritical bifurcation, saddle-node bifurcation, and Hopf bifurcation, which can deduce a standard parameter controlled relationship and in turn provide a theoretical basis for the numerical simulation. Numerical analysis ensures reliability of the theoretical results and illustrates that three stable equilibria will arise simultaneously in the model. It testifies the existence of Bogdanov-Takens bifurcation, too. It should also be stressed that the dynamic evolutionary mechanism of steady conversion and bifurcation behavior mainly depend on a specific key parameter. In a word, all these results are expected to be of use in the study of the dynamic complexity of ecosystems.

Stability, bifurcation and a new chaos in the logistic differential equation with delay

International Nuclear Information System (INIS)

Jiang Minghui; Shen Yi; Jian Jigui; Liao Xiaoxin

2006-01-01

This Letter is concerned with bifurcation and chaos in the logistic delay differential equation with a parameter r. The linear stability of the logistic equation is investigated by analyzing the associated characteristic transcendental equation. Based on the normal form approach and the center manifold theory, the formula for determining the direction of Hopf bifurcation and the stability of bifurcation periodic solution in the first bifurcation values is obtained. By theoretical analysis and numerical simulation, we found a new chaos in the logistic delay differential equation

Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection.

Science.gov (United States)

Cao, Hui; Zhou, Yicang; Ma, Zhien

2013-01-01

A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied. The condition for the global stability of the disease free equilibrium is obtained. The existence of the endemic equilibrium and its stability are investigated. More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation. Sufficient conditions for those bifurcations have been obtained. Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.

Hopf bifurcation in a dynamic IS-LM model with time delay

International Nuclear Information System (INIS)

Neamtu, Mihaela; Opris, Dumitru; Chilarescu, Constantin

2007-01-01

The paper investigates the impact of delayed tax revenues on the fiscal policy out-comes. Choosing the delay as a bifurcation parameter we study the direction and the stability of the bifurcating periodic solutions. We show when the system is stable with respect to the delay. Some numerical examples are given to confirm the theoretical results

Control of Limit Cycle Oscillations of a Two-Dimensional Aeroelastic System

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M. Ghommem

2010-01-01

Full Text Available Linear and nonlinear static feedback controls are implemented on a nonlinear aeroelastic system that consists of a rigid airfoil supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. The normal form is used to investigate the Hopf bifurcation that occurs as the freestream velocity is increased and to analytically predict the amplitude and frequency of the ensuing limit cycle oscillations (LCO. It is shown that linear control can be used to delay the flutter onset and reduce the LCO amplitude. Yet, its required gains remain a function of the speed. On the other hand, nonlinear control can be effciently implemented to convert any subcritical Hopf bifurcation into a supercritical one and to significantly reduce the LCO amplitude.

Nonlinear stability control and λ-bifurcation

International Nuclear Information System (INIS)

Erneux, T.; Reiss, E.L.; Magnan, J.F.; Jayakumar, P.K.

1987-01-01

Passive techniques for nonlinear stability control are presented for a model of fluidelastic instability. They employ the phenomena of λ-bifurcation and a generalization of it. λ-bifurcation occurs when a branch of flutter solutions bifurcates supercritically from a basic solution and terminates with an infinite period orbit at a branch of divergence solutions which bifurcates subcritically from the basic solution. The shape of the bifurcation diagram then resembles the greek letter λ. When the system parameters are in the range where flutter occurs by λ-bifurcation, then as the flow velocity increase the flutter amplitude also increases, but the frequencies of the oscillations decrease to zero. This diminishes the damaging effects of structural fatigue by flutter, and permits the flow speed to exceed the critical flutter speed. If generalized λ-bifurcation occurs, then there is a jump transition from the flutter states to a divergence state with a substantially smaller amplitude, when the flow speed is sufficiently larger than the critical flutter speed

Global Bifurcation of a Novel Computer Virus Propagation Model

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Jianguo Ren

2014-01-01

Full Text Available In a recent paper by J. Ren et al. (2012, a novel computer virus propagation model under the effect of the antivirus ability in a real network is established. The analysis there only partially uncovers the dynamics behaviors of virus spread over the network in the case where around bifurcation is local. In the present paper, by mathematical analysis, it is further shown that, under appropriate parameter values, the model may undergo a global B-T bifurcation, and the curves of saddle-node bifurcation, Hopf bifurcation, and homoclinic bifurcation are obtained to illustrate the qualitative behaviors of virus propagation. On this basis, a collection of policies is recommended to prohibit the virus prevalence. To our knowledge, this is the first time the global bifurcation has been explored for the computer virus propagation. Theoretical results and corresponding suggestions may help us suppress or eliminate virus propagation in the network.

Bifurcation analysis of nephron pressure and flow regulation

DEFF Research Database (Denmark)

Barfred, Mikael; Mosekilde, Erik; Holstein-Rathlou, N.-H.

1996-01-01

One- and two-dimensional continuation techniques are applied to study the bifurcation structure of a model of renal flow and pressure control. Integrating the main physiological mechanisms by which the individual nephron regulates the incoming blood flow, the model describes the interaction between...... the tubuloglomerular feedback and the response of the afferent arteriole. It is shown how a Hopf bifurcation leads the system to perform self-sustained oscillations if the feedback gain becomes sufficiently strong, and how a further increase of this parameter produces a folded structure of overlapping period...

Effect of nonlinear void reactivity on bifurcation characteristics of a lumped-parameter model of a BWR: A study relevant to RBMK

Energy Technology Data Exchange (ETDEWEB)

Verma, Dinkar, E-mail: dinkar@iitk.ac.in [Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016 (India); Kalra, Manjeet Singh, E-mail: drmanjeet.singh@dituniversity.edu.in [DIT University, Dehradun 248 009 (India); Wahi, Pankaj, E-mail: wahi@iitk.ac.in [Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016 (India)

2017-04-15

Highlights: • A simplified model with nonlinear void reactivity feedback is studied. • Method of multiple scales for nonlinear analysis and oscillation characteristics. • Second order void reactivity dominates in determining system dynamics. • Opposing signs of linear and quadratic void reactivity enhances global safety. - Abstract: In the present work, the effect of nonlinear void reactivity on the dynamics of a simplified lumped-parameter model for a boiling water reactor (BWR) is investigated. A mathematical model of five differential equations comprising of neutronics and thermal-hydraulics encompassing the nonlinearities associated with both the reactivity feedbacks and the heat transfer process has been used. To this end, we have considered parameters relevant to RBMK for which the void reactivity is known to be nonlinear. A nonlinear analysis of the model exploiting the method of multiple time scales (MMTS) predicts the occurrence of the two types of Hopf bifurcation, namely subcritical and supercritical, leading to the evolution of limit cycles for a range of parameters. Numerical simulations have been performed to verify the analytical results obtained by MMTS. The study shows that the nonlinear reactivity has a significant influence on the system dynamics. A parametric study with varying nominal reactor power and operating conditions in coolant channel has also been performed which shows the effect of change in concerned parameter on the boundary between regions of sub- and super-critical Hopf bifurcations in the space constituted by the two coefficients of reactivities viz. the void and the Doppler coefficient of reactivities. In particular, we find that introduction of a negative quadratic term in the void reactivity feedback significantly increases the supercritical region and dominates in determining the system dynamics.

Quasi-periodicity and chaos in a differentially heated cavity

Energy Technology Data Exchange (ETDEWEB)

Mercader, Isabel; Batiste, Oriol [Universitat Politecnica de Catalunya, Dep. Fisica Aplicada, Barcelona (Spain); Ruiz, Xavier [Univesitat Rovira i Virgili, Lab. Fisica Aplicada, Facultat de Ciencies Quimiques, Tarragona (Spain)

2004-11-01

Convective flows of a small Prandtl number fluid contained in a two-dimensional vertical cavity subject to a lateral thermal gradient are studied numerically. The chosen geometry and the values of the material parameters are relevant to semiconductor crystal growth experiments in the horizontal configuration of the Bridgman method. For increasing Rayleigh numbers we find a transition from a steady flow to periodic solutions through a supercritical Hopf bifurcation that maintains the centro-symmetry of the basic circulation. For a Rayleigh number of about ten times that of the Hopf bifurcation, the periodic solution loses stability in a subcritical Neimark-Sacker bifurcation, which gives rise to a branch of quasiperiodic states. In this branch, several intervals of frequency locking have been identified. Inside the resonance horns the stable limit cycles lose and gain stability via some typical scenarios in the bifurcation of periodic solutions. After a complicated bifurcation diagram of the stable limit cycle of the 1:10 resonance horn, a soft transition to chaos is obtained. (orig.)

Effects of positive electrical feedback in the oscillating Belousov-Zhabotinsky reaction: Experiments and simulations

International Nuclear Information System (INIS)

Sriram, K.

2006-01-01

This paper describes both the experimental and numerical investigations on the effect of positive electrical feedback in the oscillating Belovsou-Zhabotinsky (BZ) reaction under batch conditions. Positive electrical feedback causes an increase in the amplitude and period of the oscillations with the corresponding increase of the feedback strength. Oregonator model with a positive feedback term suitably incorporated in one of the dynamical variables is used to account for these experimental observations. Further, the effect of positive feedback on the Hopf points are investigated numerically by constructing the bifurcation diagrams. In the absence of feedback, for a particular stoichiometric parameter, the model exhibits both supercritical and subcritical Hopf bifurcations with canard existing near the former Hopf point. In the presence of positive feedback it is observed that (i) both the Hopf points advances, (ii) the distance between the two Hopf points decreases linearly, while the period increases exponentially with the increase of feedback strength near the Hopf points, (iii) only supercritical Hopf point without canard survives for a very strong positive feedback strength and (iv) moderate feedback strength takes the system away from limit cycle to the canard regime. These observations are explained in terms of Field-Koeroes-Noyes mechanism of the Belousov-Zhabotinsky reaction. This may be the first instance where the advancement of Hopf points due to positive feedback is clearly shown

Bifurcation diagram of a cubic three-parameter autonomous system

Directory of Open Access Journals (Sweden)

Lenka Barakova

2005-07-01

Full Text Available In this paper, we study the cubic three-parameter autonomous planar system $$displaylines{ dot x_1 = k_1 + k_2x_1 - x_1^3 - x_2,cr dot x_2 = k_3 x_1 - x_2, }$$ where $k_2, k_3$ are greater than 0. Our goal is to obtain a bifurcation diagram; i.e., to divide the parameter space into regions within which the system has topologically equivalent phase portraits and to describe how these portraits are transformed at the bifurcation boundaries. Results may be applied to the macroeconomical model IS-LM with Kaldor's assumptions. In this model existence of a stable limit cycles has already been studied (Andronov-Hopf bifurcation. We present the whole bifurcation diagram and among others, we prove existence of more difficult bifurcations and existence of unstable cycles.

Bifurcation analysis on a delayed SIS epidemic model with stage structure

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Kejun Zhuang

2007-05-01

Full Text Available In this paper, a delayed SIS (Susceptible Infectious Susceptible model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to guarantee the global existence of periodic solutions are established. Also some numerical simulations for supporting the theoretical are given.

Bifurcation analysis of a delay reaction-diffusion malware propagation model with feedback control

Science.gov (United States)

Zhu, Linhe; Zhao, Hongyong; Wang, Xiaoming

2015-05-01

With the rapid development of network information technology, information networks security has become a very critical issue in our work and daily life. This paper attempts to develop a delay reaction-diffusion model with a state feedback controller to describe the process of malware propagation in mobile wireless sensor networks (MWSNs). By analyzing the stability and Hopf bifurcation, we show that the state feedback method can successfully be used to control unstable steady states or periodic oscillations. Moreover, formulas for determining the properties of the bifurcating periodic oscillations are derived by applying the normal form method and center manifold theorem. Finally, we conduct extensive simulations on large-scale MWSNs to evaluate the proposed model. Numerical evidences show that the linear term of the controller is enough to delay the onset of the Hopf bifurcation and the properties of the bifurcation can be regulated to achieve some desirable behaviors by choosing the appropriate higher terms of the controller. Furthermore, we obtain that the spatial-temporal dynamic characteristics of malware propagation are closely related to the rate constant for nodes leaving the infective class for recovered class and the mobile behavior of nodes.

Bifurcation scenarios for bubbling transition.

Science.gov (United States)

Zimin, Aleksey V; Hunt, Brian R; Ott, Edward

2003-01-01

Dynamical systems with chaos on an invariant submanifold can exhibit a type of behavior called bubbling, whereby a small random or fixed perturbation to the system induces intermittent bursting. The bifurcation to bubbling occurs when a periodic orbit embedded in the chaotic attractor in the invariant manifold becomes unstable to perturbations transverse to the invariant manifold. Generically the periodic orbit can become transversely unstable through a pitchfork, transcritical, period-doubling, or Hopf bifurcation. In this paper a unified treatment of the four types of bubbling bifurcation is presented. Conditions are obtained determining whether the transition to bubbling is soft or hard; that is, whether the maximum burst amplitude varies continuously or discontinuously with variation of the parameter through its critical value. For soft bubbling transitions, the scaling of the maximum burst amplitude with the parameter is derived. For both hard and soft transitions the scaling of the average interburst time with the bifurcation parameter is deduced. Both random (noise) and fixed (mismatch) perturbations are considered. Results of numerical experiments testing our theoretical predictions are presented.

Multiple-parameter bifurcation analysis in a Kuramoto model with time delay and distributed shear

Science.gov (United States)

Niu, Ben; Zhang, Jiaming; Wei, Junjie

2018-05-01

In this paper, time delay effect and distributed shear are considered in the Kuramoto model. On the Ott-Antonsen's manifold, through analyzing the associated characteristic equation of the reduced functional differential equation, the stability boundary of the incoherent state is derived in multiple-parameter space. Moreover, very rich dynamical behavior such as stability switches inducing synchronization switches can occur in this equation. With the loss of stability, Hopf bifurcating coherent states arise, and the criticality of Hopf bifurcations is determined by applying the normal form theory and the center manifold theorem. On one hand, theoretical analysis indicates that the width of shear distribution and time delay can both eliminate the synchronization then lead the Kuramoto model to incoherence. On the other, time delay can induce several coexisting coherent states. Finally, some numerical simulations are given to support the obtained results where several bifurcation diagrams are drawn, and the effect of time delay and shear is discussed.

Stability and Bifurcation in Magnetic Flux Feedback Maglev Control System

Directory of Open Access Journals (Sweden)

Wen-Qing Zhang

2013-01-01

Full Text Available Nonlinear properties of magnetic flux feedback control system have been investigated mainly in this paper. We analyzed the influence of magnetic flux feedback control system on control property by time delay and interfering signal of acceleration. First of all, we have established maglev nonlinear model based on magnetic flux feedback and then discussed hopf bifurcation’s condition caused by the acceleration’s time delay. The critical value of delayed time is obtained. It is proved that the period solution exists in maglev control system and the stable condition has been got. We obtained the characteristic values by employing center manifold reduction theory and normal form method, which represent separately the direction of hopf bifurcation, the stability of the period solution, and the period of the period motion. Subsequently, we discussed the influence maglev system on stability of by acceleration’s interfering signal and obtained the stable domain of interfering signal. Some experiments have been done on CMS04 maglev vehicle of National University of Defense Technology (NUDT in Tangshan city. The results of experiments demonstrate that viewpoints of this paper are correct and scientific. When time lag reaches the critical value, maglev system will produce a supercritical hopf bifurcation which may cause unstable period motion.

Experimental study of complex mixed-mode oscillations generated in a Bonhoeffer-van der Pol oscillator under weak periodic perturbation

Energy Technology Data Exchange (ETDEWEB)

Shimizu, Kuniyasu, E-mail: kuniyasu.shimizu@it-chiba.ac.jp [Department of Electrical, Electronics and Computer Engineering, Chiba Institute of Technology, Narashino 275-0016 (Japan); Sekikawa, Munehisa [Department of Mechanical and Intelligent Engineering, Utsunomiya University, Utsunomiya 321-8585 (Japan); Inaba, Naohiko [Organization for the Strategic Coordination of Research and Intellectual Property, Meiji University, Kawasaki 214-8571 (Japan)

2015-02-15

Bifurcations of complex mixed-mode oscillations denoted as mixed-mode oscillation-incrementing bifurcations (MMOIBs) have frequently been observed in chemical experiments. In a previous study [K. Shimizu et al., Physica D 241, 1518 (2012)], we discovered an extremely simple dynamical circuit that exhibits MMOIBs. Our model was represented by a slow/fast Bonhoeffer-van der Pol circuit under weak periodic perturbation near a subcritical Andronov-Hopf bifurcation point. In this study, we experimentally and numerically verify that our dynamical circuit captures the essence of the underlying mechanism causing MMOIBs, and we observe MMOIBs and chaos with distinctive waveforms in real circuit experiments.

Bifurcation structure of a model of bursting pancreatic cells

DEFF Research Database (Denmark)

Mosekilde, Erik; Lading, B.; Yanchuk, S.

2001-01-01

One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other. The transit......One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic P-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other....... The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n + 1)-spike bursting...

Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics

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Robert Artebrant

2009-01-01

cells surrounded by collections of normal cells. Thus, the cell model features a discontinuous coefficient. Analytical techniques are applied to approximate the time-periodic solution that arises at the Hopf bifurcation point. Accurate numerical experiments are employed to complement our findings.

Self-dual Hopf quivers

International Nuclear Information System (INIS)

Huang Hualin; Li Libin; Ye Yu

2004-07-01

We study pointed graded self-dual Hopf algebras with a help of the dual Gabriel theorem for pointed Hopf algebras. Quivers of such Hopf algebras are said to be self-dual. An explicit classification of self-dual Hopf quivers is obtained. We also prove that finite dimensional coradically graded pointed self-dual Hopf algebras are generated by group-like and skew-primitive elements as associative algebras. This partially justifies a conjecture of Andruskiewitsch and Schneider and may help to classify finite dimensional self-dual pointed Hopf algebras

Oscillatory bistability of real-space transfer in semiconductor heterostructures

Science.gov (United States)

Do˙ttling, R.; Scho˙ll, E.

1992-01-01

Charge transport parallel to the layers of a modulation-doped GaAs/AlxGa1-xAs heterostructure is studied theoretically. The heating of electrons by the applied electric field leads to real-space transfer of electrons from the GaAs into the adjacent AlxGa1-xAs layer. For sufficiently large dc bias, spontaneous periodic 100-GHz current oscillations, and bistability and hysteretic switching transitions between oscillatory and stationary states are predicted. We present a detailed investigation of complex bifurcation scenarios as a function of the bias voltage U0 and the load resistance RL. For large RL subcritical Hopf bifurcations and global bifurcations of limit cycles are displayed.

Bifurcación de hopf en un modelo sobre resistencia bacteriana

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Saulo Mosquera-Lopez

2013-01-01

Full Text Available In 2011 Romero J. in his master’s thesis “Mathematical models for bacterial resistance to antibiotics” formulated and analyzed a nonlinear system of ordinary differential equations describing the acquisition of bacterial resistance through two mechanisms: action plasmids and treatment with antibiotics. Under certain conditions the system has three equilibrium points and one of them coexist both sensitive and resistant bacteria. Numerical simulations performed in this work suggest that around this equilibrium point exists a Hopf bifurcation. From these observations we have developed a project which aims to analyze the conditions to be satisfied by the parameters of the model, to ensure the existence of this bifurcation and classify their stability. The main objective of the conference is to present the progress made in the development of this project.

Stability and Bifurcation of a Fishery Model with Crowley-Martin Functional Response

Science.gov (United States)

Maiti, Atasi Patra; Dubey, B.

To understand the dynamics of a fishery system, a nonlinear mathematical model is proposed and analyzed. In an aquatic environment, we considered two populations: one is prey and another is predator. Here both the fish populations grow logistically and interaction between them is of Crowley-Martin type functional response. It is assumed that both the populations are harvested and the harvesting effort is assumed to be dynamical variable and tax is considered as a control variable. The existence of equilibrium points and their local stability are examined. The existence of Hopf-bifurcation, stability and direction of Hopf-bifurcation are also analyzed with the help of Center Manifold theorem and normal form theory. The global stability behavior of the positive equilibrium point is also discussed. In order to find the value of optimal tax, the optimal harvesting policy is used. To verify our analytical findings, an extensive numerical simulation is carried out for this model system.

Variants of bosonization in parabosonic algebra: the Hopf and super-Hopf structures in parabosonic algebra

International Nuclear Information System (INIS)

Kanakoglou, K; Daskaloyannis, C

2008-01-01

Parabosonic algebra in finite or infinite degrees of freedom is considered as a Z 2 -graded associative algebra, and is shown to be a Z 2 -graded (or super) Hopf algebra. The super-Hopf algebraic structure of the parabosonic algebra is established directly without appealing to its relation to the osp(1/2n) Lie superalgebraic structure. The notion of super-Hopf algebra is equivalently described as a Hopf algebra in the braided monoidal category CZ 2 M. The bosonization technique for switching a Hopf algebra in the braided monoidal category H M (where H is a quasitriangular Hopf algebra) into an ordinary Hopf algebra is reviewed. In this paper, we prove that for the parabosonic algebra P B , beyond the application of the bosonization technique to the original super-Hopf algebra, a bosonization-like construction is also achieved using two operators, related to the parabosonic total number operator. Both techniques switch the same super-Hopf algebra P B to an ordinary Hopf algebra, thus producing two different variants of P B , with an ordinary Hopf structure

Bifurcation analysis of a product inhibition model of a continuous fermentation process

Energy Technology Data Exchange (ETDEWEB)

Lenbury, Y; Chiaranai, C

1987-03-01

A product inhibition model of a continuous fermentation process is considered. If the yield term is a variable function of ethanol concentration, oscillation in the cell and ethanol concentrations is shown to be a Hopf bifurcation in the underlying system of nonlinear, ordinary differential equations which comprises the model.

The formal theory of Hopf algebras part II: the case of Hopf algebras ...

African Journals Online (AJOL)

The category HopfR of Hopf algebras over a commutative unital ring R is analyzed with respect to its categorical properties. The main results are: (1) For every ring R the category HopfR is locally presentable, it is coreflective in the category of bialgebras over R, over every R-algebra there exists a cofree Hopf algebra. (2) If ...

Bistability of bursting and silence regimes in a model of a leech heart interneuron

Science.gov (United States)

Malashchenko, Tatiana; Shilnikov, Andrey; Cymbalyuk, Gennady

2011-10-01

Bursting is one of the primary activity regimes of neurons. Our study is focused on determining a generic biophysical mechanism underlying the coexistence of the bursting and silent regimes observed in a neuron model. We show that the main ingredient for this mechanism is a saddle periodic orbit. The stable manifold of the orbit sets a threshold between the regimes of activity. Thus, the range of the controlling parameters, where the coexistence is observed, is limited by the bifurcations' values at which the saddle orbit appears and disappears. We show that it appears through the subcritical Andronov-Hopf bifurcation, where the equilibrium representing the silent regime loses stability, and disappears at the homoclinic bifurcation. Correspondingly, the bursting regime disappears in close proximity to the homoclinic bifurcation.

Dynamical Analysis of the Lorenz-84 Atmospheric Circulation Model

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Hu Wang

2014-01-01

Full Text Available The dynamical behaviors of the Lorenz-84 atmospheric circulation model are investigated based on qualitative theory and numerical simulations. The stability and local bifurcation conditions of the Lorenz-84 atmospheric circulation model are obtained. It is also shown that when the bifurcation parameter exceeds a critical value, the Hopf bifurcation occurs in this model. Then, the conditions of the supercritical and subcritical bifurcation are derived through the normal form theory. Finally, the chaotic behavior of the model is also discussed, the bifurcation diagrams and Lyapunov exponents spectrum for the corresponding parameter are obtained, and the parameter interval ranges of limit cycle and chaotic attractor are calculated in further. Especially, a computer-assisted proof of the chaoticity of the model is presented by a topological horseshoe theory.

Simplest bifurcation diagrams for monotone families of vector fields on a torus

Science.gov (United States)

Baesens, C.; MacKay, R. S.

2018-06-01

In part 1, we prove that the bifurcation diagram for a monotone two-parameter family of vector fields on a torus has to be at least as complicated as the conjectured simplest one proposed in Baesens et al (1991 Physica D 49 387–475). To achieve this, we define ‘simplest’ by sequentially minimising the numbers of equilibria, Bogdanov–Takens points, closed curves of centre and of neutral saddle, intersections of curves of centre and neutral saddle, Reeb components, other invariant annuli, arcs of rotational homoclinic bifurcation of horizontal homotopy type, necklace points, contractible periodic orbits, points of neutral horizontal homoclinic bifurcation and half-plane fan points. We obtain two types of simplest case, including that initially proposed. In part 2, we analyse the bifurcation diagram for an explicit monotone family of vector fields on a torus and prove that it has at most two equilibria, precisely four Bogdanov–Takens points, no closed curves of centre nor closed curves of neutral saddle, at most two Reeb components, precisely four arcs of rotational homoclinic connection of ‘horizontal’ homotopy type, eight horizontal saddle-node loop points, two necklace points, four points of neutral horizontal homoclinic connection, and two half-plane fan points, and there is no simultaneous existence of centre and neutral saddle, nor contractible homoclinic connection to a neutral saddle. Furthermore, we prove that all saddle-nodes, Bogdanov–Takens points, non-neutral and neutral horizontal homoclinic bifurcations are non-degenerate and the Hopf condition is satisfied for all centres. We also find it has four points of degenerate Hopf bifurcation. It thus provides an example of a family satisfying all the assumptions of part 1 except the one of at most one contractible periodic orbit.

A simple delay model for two-phase flow dynamics

Energy Technology Data Exchange (ETDEWEB)

Clausse, A.; Delmastro, D.F.; Juanico`, L.E. [Centro Atomico Bariloche (Argentina)

1995-09-01

A model based in delay equations for density-wave oscillations is presented. High Froude numbers and moderate ones were considered. The equations were numerically analyzed and compared with more sophisticated models. The influence of the gravity term was studied. Different kinds of behavior were found, particularly sub-critical and super-critical Hopf bifurcations. Moreover the present approach can be used to better understand the complicated dynamics of boiling flows systems.

Bifurcation and Fractal of the Coupled Logistic Map

Science.gov (United States)

Wang, Xingyuan; Luo, Chao

The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot-Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.

Bursting oscillations, bifurcation and synchronization in neuronal systems

Energy Technology Data Exchange (ETDEWEB)

Wang Haixia [School of Science, Nanjing University of Science and Technology, Nanjing 210094 (China); Wang Qingyun, E-mail: drwangqy@gmail.com [Department of Dynamics and Control, Beihang University, Beijing 100191 (China); Lu Qishao [Department of Dynamics and Control, Beihang University, Beijing 100191 (China)

2011-08-15

Highlights: > We investigate bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. > Two types of fast-slow bursters are analyzed in detail. > We show the properties of some crucial bifurcation points. > Synchronization transition and the neural excitability are explored in the coupled bursters. - Abstract: This paper investigates bursting oscillations and related bifurcation in the modified Morris-Lecar neuron. It is shown that for some appropriate parameters, the modified Morris-Lecar neuron can exhibit two types of fast-slow bursters, that is 'circle/fold cycle' bursting and 'subHopf/homoclinic' bursting with class 1 and class 2 neural excitability, which have different neuro-computational properties. By means of the analysis of fast-slow dynamics and phase plane, we explore bifurcation mechanisms associated with the two types of bursters. Furthermore, the properties of some crucial bifurcation points, which can determine the type of the burster, are studied by the stability and bifurcation theory. In addition, we investigate the influence of the coupling strength on synchronization transition and the neural excitability in two electrically coupled bursters with the same bursting type. More interestingly, the multi-time-scale synchronization transition phenomenon is found as the coupling strength varies.

Bifurcation analysis of a delayed mathematical model for tumor growth

International Nuclear Information System (INIS)

Khajanchi, Subhas

2015-01-01

In this study, we present a modified mathematical model of tumor growth by introducing discrete time delay in interaction terms. The model describes the interaction between tumor cells, healthy tissue cells (host cells) and immune effector cells. The goal of this study is to obtain a better compatibility with reality for which we introduced the discrete time delay in the interaction between tumor cells and host cells. We investigate the local stability of the non-negative equilibria and the existence of Hopf-bifurcation by considering the discrete time delay as a bifurcation parameter. We estimate the length of delay to preserve the stability of bifurcating periodic solutions, which gives an idea about the mode of action for controlling oscillations in the tumor growth. Numerical simulations of the model confirm the analytical findings

Emergence of the bifurcation structure of a Langmuir–Blodgett transfer model

KAUST Repository

Köpf, Michael H

2014-10-07

© 2014 IOP Publishing Ltd & London Mathematical Society. We explore the bifurcation structure of a modified Cahn-Hilliard equation that describes a system that may undergo a first-order phase transition and is kept permanently out of equilibrium by a lateral driving. This forms a simple model, e.g., for the deposition of stripe patterns of different phases of surfactant molecules through Langmuir-Blodgett transfer. Employing continuation techniques the bifurcation structure is numerically investigated using the non-dimensional transfer velocity as the main control parameter. It is found that the snaking structure of steady front states is intertwined with a large number of branches of time-periodic solutions that emerge from Hopf or period-doubling bifurcations and end in global bifurcations (sniper and homoclinic). Overall the bifurcation diagram has a harp-like appearance. This is complemented by a two-parameter study in non-dimensional transfer velocity and domain size (as a measure of the distance to the phase transition threshold) that elucidates through which local and global codimension 2 bifurcations the entire harp-like structure emerges.

Bifurcation analysis of Rössler system with multiple delayed feedback

Directory of Open Access Journals (Sweden)

Meihong Xu

2010-10-01

Full Text Available In this paper, regarding the delay as parameter, we investigate the effect of delay on the dynamics of a Rössler system with multiple delayed feedback proposed by Ghosh and Chowdhury. At first we consider the stability of equilibrium and the existence of Hopf bifurcations. Then an explicit algorithm for determining the direction and the stability of the bifurcating periodic solutions is derived by using the normal form theory and center manifold argument. Finally, we give a numerical simulation example which indicates that chaotic oscillation is converted into a stable steady state or a stable periodic orbit when the delay passes through certain critical values.

Turing-Hopf bifurcations in a predator-prey model with herd behavior, quadratic mortality and prey-taxis

Science.gov (United States)

Liu, Xia; Zhang, Tonghua; Meng, Xinzhu; Zhang, Tongqian

2018-04-01

In this paper, we propose a predator-prey model with herd behavior and prey-taxis. Then, we analyze the stability and bifurcation of the positive equilibrium of the model subject to the homogeneous Neumann boundary condition. By using an abstract bifurcation theory and taking prey-tactic sensitivity coefficient as the bifurcation parameter, we obtain a branch of stable nonconstant solutions bifurcating from the positive equilibrium. Our results show that prey-taxis can yield the occurrence of spatial patterns.

Bifurcation in Z2-symmetry quadratic polynomial systems with delay

International Nuclear Information System (INIS)

Zhang Chunrui; Zheng Baodong

2009-01-01

Z 2 -symmetry systems are considered. Firstly the general forms of Z 2 -symmetry quadratic polynomial system are given, and then a three-dimensional Z 2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.

Quasi-periodic bifurcations and “amplitude death” in low-dimensional ensemble of van der Pol oscillators

Energy Technology Data Exchange (ETDEWEB)

Emelianova, Yu.P., E-mail: yuliaem@gmail.com [Department of Electronics and Instrumentation, Saratov State Technical University, Polytechnicheskaya 77, Saratov 410054 (Russian Federation); Kuznetsov, A.P., E-mail: apkuz@rambler.ru [Kotel' nikov' s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelyenaya 38, Saratov 410019 (Russian Federation); Turukina, L.V., E-mail: lvtur@rambler.ru [Kotel' nikov' s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, Zelyenaya 38, Saratov 410019 (Russian Federation); Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam (Germany)

2014-01-10

The dynamics of the four dissipatively coupled van der Pol oscillators is considered. Lyapunov chart is presented in the parameter plane. Its arrangement is discussed. We discuss the bifurcations of tori in the system at large frequency detuning of the oscillators. Here are quasi-periodic saddle-node, Hopf and Neimark–Sacker bifurcations. The effect of increase of the threshold for the “amplitude death” regime and the possibilities of complete and partial broadband synchronization are revealed.

Bifurcation and chaos in neural excitable system

International Nuclear Information System (INIS)

Jing Zhujun; Yang Jianping; Feng Wei

2006-01-01

In this paper, we investigate the dynamical behaviors of neural excitable system without periodic external current (proposed by Chialvo [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] and with periodic external current as system's parameters vary. The existence and stability of three fixed points, bifurcation of fixed points, the conditions of existences of fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using bifurcation theory and center manifold theorem. The chaotic existence in the sense of Marotto's definition of chaos is proved. We then give the numerical simulated results (using bifurcation diagrams, computations of Maximum Lyapunov exponent and phase portraits), which not only show the consistence with the analytic results but also display new and interesting dynamical behaviors, including the complete period-doubling and inverse period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, simultaneous occurrence of two different routes (invariant cycle and period-doubling bifurcations) to chaos for a given bifurcation parameter, sudden disappearance of chaos at one critical point, a great abundance of period windows (period 2 to 10, 12, 19, 20 orbits, and so on) in transient chaotic regions with interior crises, strange chaotic attractors and strange non-chaotic attractor. In particular, the parameter k plays a important role in the system, which can leave the chaotic behavior or the quasi-periodic behavior to period-1 orbit as k varies, and it can be considered as an control strategy of chaos by adjusting the parameter k. Combining the existing results in [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] with the new results reported in this paper, a more complete description of the system is now obtained

Hopf algebras in noncommutative geometry

International Nuclear Information System (INIS)

Varilly, Joseph C.

2001-10-01

We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)

Turing instability and bifurcation analysis in a diffusive bimolecular system with delayed feedback

Science.gov (United States)

Wei, Xin; Wei, Junjie

2017-09-01

A diffusive autocatalytic bimolecular model with delayed feedback subject to Neumann boundary conditions is considered. We mainly study the stability of the unique positive equilibrium and the existence of periodic solutions. Our study shows that diffusion can give rise to Turing instability, and the time delay can affect the stability of the positive equilibrium and result in the occurrence of Hopf bifurcations. By applying the normal form theory and center manifold reduction for partial functional differential equations, we investigate the stability and direction of the bifurcations. Finally, we give some simulations to illustrate our theoretical results.

Stability and bifurcation analysis of an SIR epidemic model with logistic growth and saturated treatment

International Nuclear Information System (INIS)

Li, Jinhui; Teng, Zhidong; Wang, Guangqing; Zhang, Long; Hu, Cheng

2017-01-01

In this paper, we introduce the saturated treatment and logistic growth rate into an SIR epidemic model with bilinear incidence. The treatment function is assumed to be a continuously differential function which describes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is large enough. Sufficient conditions for the existence and local stability of the disease-free and positive equilibria are established. And the existence of the stable limit cycles also is obtained. Moreover, by using the theory of bifurcations, it is shown that the model exhibits backward bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcations. Finally, the numerical examples are given to illustrate the theoretical results and obtain some additional interesting phenomena, involving double stable periodic solutions and stable limit cycles.

Bifurcation analysis of magnetization dynamics driven by spin transfer

International Nuclear Information System (INIS)

Bertotti, G.; Magni, A.; Bonin, R.; Mayergoyz, I.D.; Serpico, C.

2005-01-01

Nonlinear magnetization dynamics under spin-polarized currents is discussed by the methods of the theory of nonlinear dynamical systems. The fixed points of the dynamics are calculated. It is shown that there may exist 2, 4, or 6 fixed points depending on the values of the external field and of the spin-polarized current. The stability of the fixed points is analyzed and the conditions for the occurrence of saddle-node and Hopf bifurcations are determined

Bifurcation analysis of magnetization dynamics driven by spin transfer

Energy Technology Data Exchange (ETDEWEB)

Bertotti, G. [IEN Galileo Ferraris, Strada delle Cacce 91, 10135 Turin (Italy); Magni, A. [IEN Galileo Ferraris, Strada delle Cacce 91, 10135 Turin (Italy); Bonin, R. [Dipartimento di Fisica, Politecnico di Torino, Corso degli Abbruzzi, 10129 Turin (Italy)]. E-mail: bonin@ien.it; Mayergoyz, I.D. [Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742 (United States); Serpico, C. [Department of Electrical Engineering, University of Napoli Federico II, via Claudio 21, 80125 Naples (Italy)

2005-04-15

Nonlinear magnetization dynamics under spin-polarized currents is discussed by the methods of the theory of nonlinear dynamical systems. The fixed points of the dynamics are calculated. It is shown that there may exist 2, 4, or 6 fixed points depending on the values of the external field and of the spin-polarized current. The stability of the fixed points is analyzed and the conditions for the occurrence of saddle-node and Hopf bifurcations are determined.

On a Five-Dimensional Chaotic System Arising from Double-Diffusive Convection in a Fluid Layer

Directory of Open Access Journals (Sweden)

R. Idris

2013-01-01

Full Text Available A chaotic system arising from double-diffusive convection in a fluid layer is investigated in this paper based on the theory of dynamical systems. A five-dimensional model of chaotic system is obtained using the Galerkin truncated approximation. The results showed that the transition from steady convection to chaos via a Hopf bifurcation produced a limit cycle which may be associated with a homoclinic explosion at a slightly subcritical value of the Rayleigh number.

Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions

Science.gov (United States)

Barnett, William A.; Duzhak, Evgeniya Aleksandrovna

2008-06-01

Grandmont [J.M. Grandmont, On endogenous competitive business cycles, Econometrica 53 (1985) 995-1045] found that the parameter space of the most classical dynamic models is stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with many forms of multiperiodic dynamics in between. The econometric implications of Grandmont’s findings are particularly important, if bifurcation boundaries cross the confidence regions surrounding parameter estimates in policy-relevant models. Stratification of a confidence region into bifurcated subsets seriously damages robustness of dynamical inferences. Recently, interest in policy in some circles has moved to New-Keynesian models. As a result, in this paper we explore bifurcation within the class of New-Keynesian models. We develop the econometric theory needed to locate bifurcation boundaries in log-linearized New-Keynesian models with Taylor policy rules or inflation-targeting policy rules. Central results needed in this research are our theorems on the existence and location of Hopf bifurcation boundaries in each of the cases that we consider.

Stochastic Bifurcation Analysis of an Elastically Mounted Flapping Airfoil

Directory of Open Access Journals (Sweden)

Bose Chandan

2018-01-01

Full Text Available The present paper investigates the effects of noisy flow fluctuations on the fluid-structure interaction (FSI behaviour of a span-wise flexible wing modelled as a two degree-of-freedom elastically mounted flapping airfoil. In the sterile flow conditions, the system undergoes a Hopf bifurcation as the free-stream velocity exceeds a critical limit resulting in a stable limit-cycle oscillation (LCO from a fixed point response. On the other hand, the qualitative dynamics changes from a stochastic fixed point to a random LCO through an intermittent state in the presence of irregular flow fluctuations. The probability density function depicts the most probable system state in the phase space. A phenomenological bifurcation (P-bifurcation analysis based on the transition in the topology associated with the structure of the joint probability density function (pdf of the response variables has been carried out. The joint pdf corresponding to the stochastic fixed point possesses a Dirac delta function like structure with a sharp single peak around zero. As the mean flow speed crosses the critical value, the joint pdf bifurcates to a crater-like structure indicating the occurrence of a P-bifurcation. The intermittent state is characterized by the co-existence of the unimodal as well as the crater like structure.

Bifurcation and category learning in network models of oscillating cortex

Science.gov (United States)

Baird, Bill

1990-06-01

A genetic model of oscillating cortex, which assumes “minimal” coupling justified by known anatomy, is shown to function as an associative memory, using previously developed theory. The network has explicit excitatory neurons with local inhibitory interneuron feedback that forms a set of nonlinear oscillators coupled only by long-range excitatory connections. Using a local Hebb-like learning rule for primary and higher-order synapses at the ends of the long-range connections, the system learns to store the kinds of oscillation amplitude patterns observed in olfactory and visual cortex. In olfaction, these patterns “emerge” during respiration by a pattern forming phase transition which we characterize in the model as a multiple Hopf bifurcation. We argue that these bifurcations play an important role in the operation of real digital computers and neural networks, and we use bifurcation theory to derive learning rules which analytically guarantee CAM storage of continuous periodic sequences-capacity: N/2 Fourier components for an N-node network-no “spurious” attractors.

Weak C* Hopf Symmetry

OpenAIRE

Rehren, K. -H.

1996-01-01

Weak C* Hopf algebras can act as global symmetries in low-dimensional quantum field theories, when braid group statistics prevents group symmetries. Possibilities to construct field algebras with weak C* Hopf symmetry from a given theory of local observables are discussed.

Synchronization and symmetry-breaking bifurcations in constructive networks of coupled chaotic oscillators

International Nuclear Information System (INIS)

Jiang Yu; Lozada-Cassou, M.; Vinet, A.

2003-01-01

The spatiotemporal dynamics of networks based on a ring of coupled oscillators with regular shortcuts beyond the nearest-neighbor couplings is studied by using master stability equations and numerical simulations. The generic criterion for dynamic synchronization has been extended to arbitrary network topologies with zero row-sum. The symmetry-breaking oscillation patterns that resulted from the Hopf bifurcation from synchronous states are analyzed by the symmetry group theory

Hopf solitons in the AFZ model

International Nuclear Information System (INIS)

Gillard, Mike

2011-01-01

The Aratyn–Ferreira–Zimerman (AFZ) model is a conformal field theory in three-dimensional space. It has solutions that are topological solitons classified by an integer-valued Hopf index. There exist infinitely many axial solutions which have been found analytically. Static axial, knot and linked solitons are found numerically using a modified volume preserving flow for Hopf index one to eight, allowing for comparison with other Hopf soliton models. Solutions include a static trefoil knot at Hopf index five. A one-parameter family of conformal Skyrme–Faddeev models, consisting of linear combinations of the Nicole and AFZ models, are also investigated numerically. The transition of solutions for Hopf index four is mapped across these models. A topological change between linked and axial solutions occurs, with fewer models (or a limited range of parameter values) permitting axial solitons than linked solitons at Hopf index four

Modelling, singular perturbation and bifurcation analyses of bitrophic food chains.

Science.gov (United States)

Kooi, B W; Poggiale, J C

2018-04-20

Two predator-prey model formulations are studied: for the classical Rosenzweig-MacArthur (RM) model and the Mass Balance (MB) chemostat model. When the growth and loss rate of the predator is much smaller than that of the prey these models are slow-fast systems leading mathematically to singular perturbation problem. In contradiction to the RM-model, the resource for the prey are modelled explicitly in the MB-model but this comes with additional parameters. These parameter values are chosen such that the two models become easy to compare. In both models a transcritical bifurcation, a threshold above which invasion of predator into prey-only system occurs, and the Hopf bifurcation where the interior equilibrium becomes unstable leading to a stable limit cycle. The fast-slow limit cycles are called relaxation oscillations which for increasing differences in time scales leads to the well known degenerated trajectories being concatenations of slow parts of the trajectory and fast parts of the trajectory. In the fast-slow version of the RM-model a canard explosion of the stable limit cycles occurs in the oscillatory region of the parameter space. To our knowledge this type of dynamics has not been observed for the RM-model and not even for more complex ecosystem models. When a bifurcation parameter crosses the Hopf bifurcation point the amplitude of the emerging stable limit cycles increases. However, depending of the perturbation parameter the shape of this limit cycle changes abruptly from one consisting of two concatenated slow and fast episodes with small amplitude of the limit cycle, to a shape with large amplitude of which the shape is similar to the relaxation oscillation, the well known degenerated phase trajectories consisting of four episodes (concatenation of two slow and two fast). The canard explosion point is accurately predicted by using an extended asymptotic expansion technique in the perturbation and bifurcation parameter simultaneously where the small

Bifurcation analysis in the diffusive Lotka-Volterra system: An application to market economy

International Nuclear Information System (INIS)

Wijeratne, A.W.; Yi Fengqi; Wei Junjie

2009-01-01

A diffusive Lotka-Volterra system is formulated in this paper that represents the dynamics of market share at duopoly. A case in Sri Lankan mobile telecom market was considered that conceptualized the model in interest. Detailed Hopf bifurcation, transcritical and pitchfork bifurcation analysis were performed. The distribution of roots of the characteristic equation suggests that a stable coexistence equilibrium can be achieved by increasing the innovation while minimizing competition by each competitor while regulating existing policies and introducing new ones for product differentiation and value addition. The avenue is open for future research that may use real time information in order to formulate mathematically sound tools for decision making in competitive business environments.

Bifurcation analysis in the diffusive Lotka-Volterra system: An application to market economy

Energy Technology Data Exchange (ETDEWEB)

Wijeratne, A.W. [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China); Department of Agri-Business Management, Sabaragamuwa University of Sri Lanka, Belihuloya 70140 (Sri Lanka); Yi Fengqi [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China); Wei Junjie [Department of Mathematics, Harbin Institute of Technology, Harbin 150001 (China)], E-mail: weijj@hit.edu.cn

2009-04-30

A diffusive Lotka-Volterra system is formulated in this paper that represents the dynamics of market share at duopoly. A case in Sri Lankan mobile telecom market was considered that conceptualized the model in interest. Detailed Hopf bifurcation, transcritical and pitchfork bifurcation analysis were performed. The distribution of roots of the characteristic equation suggests that a stable coexistence equilibrium can be achieved by increasing the innovation while minimizing competition by each competitor while regulating existing policies and introducing new ones for product differentiation and value addition. The avenue is open for future research that may use real time information in order to formulate mathematically sound tools for decision making in competitive business environments.

Nonlinear dynamics and bifurcation characteristics of shape memory alloy thin films subjected to in-plane stochastic excitation

International Nuclear Information System (INIS)

Zhu, Zhi-Wen; Zhang, Qing-Xin; Xu, Jia

2014-01-01

A kind of shape memory alloy (SMA) hysteretic nonlinear model was developed, and the nonlinear dynamics and bifurcation characteristics of the SMA thin film subjected to in-plane stochastic excitation were investigated. Van der Pol difference item was introduced to describe the hysteretic phenomena of the SMA strain–stress curves, and the nonlinear dynamic model of the SMA thin film subjected to in-plane stochastic excitation was developed. The conditions of global stochastic stability of the system were determined in singular boundary theory, and the probability density function of the system response was obtained. Finally, the conditions of stochastic Hopf bifurcation were analyzed. The results of theoretical analysis and numerical simulation indicate that self-excited vibration is induced by the hysteretic nonlinear characteristics of SMA, and stochastic Hopf bifurcation appears when the bifurcation parameter was changed; there are two limit cycles in the stationary probability density of the dynamic response of the system in some cases, which means that there are two vibration amplitudes whose probabilities are both very high, and jumping phenomena between the two vibration amplitudes appear with the change in conditions. The results obtained in this current paper are helpful for the application of the SMA thin film in stochastic vibration fields. - Highlights: • Hysteretic nonlinear model of shape memory alloy was developed. • Van der Pol item was introduced to interpret hysteretic strain–stress curves. • Nonlinear dynamic characteristics of the shape memory alloy film were analyzed. • Jumping phenomena were observed in the change of the parameters

Numerical exploration of Kaldorian interregional macrodynamics: stability and the trade threshold for business cycles under fixed exchange rates.

Science.gov (United States)

Asada, Toichiro; Douskos, Christos; Markellos, Panagiotis

2011-01-01

The stability of equilibrium and the possibility of generation of business cycles in a discrete interregional Kaldorian macrodynamic model with fixed exchange rates are explored using numerical methods. One of the aims is to illustrate the feasibility and effectiveness of the numerical approach for dynamical systems of moderately high dimensionality and several parameters. The model considered is five-dimensional with four parameters, the speeds of adjustment of the goods markets and the degrees of economic interactions between the regions through trade and capital movement. Using a grid search method for the determination of the region of stability of equilibrium in two-dimensional parameter subspaces, and coefficient criteria for the flip bifurcation - and Hopf bifurcation - curve, we determine the stability region in several parameter ranges and identify Hopf bifurcation curves when they exist. It is found that interregional cycles emerge only for sufficient interregional trade. The relevant threshold is predicted by the model at 14 - 16 % of trade transactions. By contrast, no minimum level of capital mobility exists in a global sense as a requirement for the emergence of interregional cycles; the main conclusion being, therefore, that cycles may occur for very low levels of capital mobility if trade is sufficient. Examples of bifurcation and Lyapunov exponent diagrams illustrating the occurrence of cycles or period doubling, and examples of the development of the occurring cycles, are given. Both supercritical and subcritical bifurcations are found to occur, the latter type indicating coexistence of a point and a cyclical attractor.

Experimental Investigation of Bifurcations in a Thermoacoustic Engine

Directory of Open Access Journals (Sweden)

Vishnu R. Unni

2015-06-01

Full Text Available In this study, variation in the characteristics of the pressure oscillations in a thermoacoustic engine is explored as the input heat flux is varied. A bifurcation diagram is plotted to study the variation in the qualitative behavior of the acoustic oscillations as the input heat flux changes. At a critical input heat flux (60 Watt, the engine begins to produce acoustic oscillations in its fundamental longitudinal mode. As the input heat flux is increased, incommensurate frequencies appear in the power spectrum. The simultaneous presence of incommensurate frequencies results in quasiperiodic oscillations. On further increase of heat flux, the fundamental mode disappears and second mode oscillations are observed. These bifurcations in the characteristics of the pressure oscillations are the result of nonlinear interaction between multiple modes present in the thermoacoustic engine. Hysteresis in the bifurcation diagram suggests that the bifurcation is subcritical. Further, the qualitative analysis of different dynamic regimes is performed using nonlinear time series analysis. The physical reason for the observed nonlinear behavior is discussed. Suggestions to avert the variations in qualitative behavior of the pressure oscillations in thermoacoustic engines are also provided.

Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays

Directory of Open Access Journals (Sweden)

2006-01-01

Full Text Available We consider a simplified bidirectional associated memory (BAM neural network model with four neurons and multiple time delays. The global existence of periodic solutions bifurcating from Hopf bifurcations is investigated by applying the global Hopf bifurcation theorem due to Wu and Bendixson's criterion for high-dimensional ordinary differential equations due to Li and Muldowney. It is shown that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of the sum of two delays. Numerical simulations supporting the theoretical analysis are also included.

Nonlinear Characteristics of Randomly Excited Transonic Flutter

DEFF Research Database (Denmark)

Christiansen, Lasse Engbo; Lehn-Schiøler, Tue; Mosekilde, Erik

2002-01-01

. When this model is extended by the introduction of nonlinear terms, it can reproduce the subcritical Hopf bifurcation. We hereafter consider the effects of subjecting simplified versions of the model to random external excitations representing the fluctuations present in the airflow. These models can......The paper describes the effects of random external excitations on the onset and dynamical characteristics of transonic flutter (i.e. large-amplitude, self-sustained oscillations) for a high aspect ratio wing. Wind tunnel experiments performed at the National Aerospace Laboratory (NAL) in Japan have...

Advance elements of optoisolation circuits nonlinearity applications in engineering

CERN Document Server

Aluf, Ofer

2017-01-01

This book on advanced optoisolation circuits for nonlinearity applications in engineering addresses two separate engineering and scientific areas, and presents advanced analysis methods for optoisolation circuits that cover a broad range of engineering applications. The book analyzes optoisolation circuits as linear and nonlinear dynamical systems and their limit cycles, bifurcation, and limit cycle stability by using Floquet theory. Further, it discusses a broad range of bifurcations related to optoisolation systems: cusp-catastrophe, Bautin bifurcation, Andronov-Hopf bifurcation, Bogdanov-Takens (BT) bifurcation, fold Hopf bifurcation, Hopf-Hopf bifurcation, Torus bifurcation (Neimark-Sacker bifurcation), and Saddle-loop or Homoclinic bifurcation. Floquet theory helps as to analyze advance optoisolation systems. Floquet theory is the study of the stability of linear periodic systems in continuous time. Another way to describe Floquet theory, it is the study of linear systems of differential equations with p...

Bifurcation and spatial pattern formation in spreading of disease with incubation period in a phytoplankton dynamics

Directory of Open Access Journals (Sweden)

Randhir Singh Baghel

2012-02-01

Full Text Available In this article, we propose a three dimensional mathematical model of phytoplankton dynamics with the help of reaction-diffusion equations that studies the bifurcation and pattern formation mechanism. We provide an analytical explanation for understanding phytoplankton dynamics with three population classes: susceptible, incubated, and infected. This model has a Holling type II response function for the population transformation from susceptible to incubated class in an aquatic ecosystem. Our main goal is to provide a qualitative analysis of Hopf bifurcation mechanisms, taking death rate of infected phytoplankton as bifurcation parameter, and to study further spatial patterns formation due to spatial diffusion. Here analytical findings are supported by the results of numerical experiments. It is observed that the coexistence of all classes of population depends on the rate of diffusion. Also we obtained the time evaluation pattern formation of the spatial system.

Hopf Structures on Standard Young Tableaux

International Nuclear Information System (INIS)

Loday, Jean-Louis; Popov, Todor

2010-01-01

We review the Poirier-Reutenauer Hopf structure on Standard Young Tableaux and show that it is a distinguished member of a family of Hopf structures. The family in question is related to deformed parastatistics.

Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film-shape memory alloy composite cantilever plate subjected to in-plane harmonic and stochastic excitation

International Nuclear Information System (INIS)

Zhu, Zhiwen; Zhang, Qingxin; Xu, Jia

2014-01-01

Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film–shape memory alloy (GMF–SMA) composite cantilever plate subjected to in-plane harmonic and stochastic excitation were studied. Van der Pol items were improved to interpret the hysteretic phenomena of both GMF and SMA, and the nonlinear dynamic model of a GMF–SMA composite cantilever plate subjected to in-plane harmonic and stochastic excitation was developed. The probability density function of the dynamic response of the system was obtained, and the conditions of stochastic Hopf bifurcation were analyzed. The conditions of noise-induced chaotic response were obtained in the stochastic Melnikov integral method, and the fractal boundary of the safe basin of the system was provided. Finally, the chaos control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that stochastic Hopf bifurcation and chaos appear in the parameter variation process. The boundary of the safe basin of the system has fractal characteristics, and its area decreases when the noise intensifies. The system reliability was improved through stochastic optimal control, and the safe basin area of the system increased

Dynamics and Physiological Roles of Stochastic Firing Patterns Near Bifurcation Points

Science.gov (United States)

Jia, Bing; Gu, Huaguang

2017-06-01

Different stochastic neural firing patterns or rhythms that appeared near polarization or depolarization resting states were observed in biological experiments on three nervous systems, and closely matched those simulated near bifurcation points between stable equilibrium point and limit cycle in a theoretical model with noise. The distinct dynamics of spike trains and interspike interval histogram (ISIH) of these stochastic rhythms were identified and found to build a relationship to the coexisting behaviors or fixed firing frequency of four different types of bifurcations. Furthermore, noise evokes coherence resonances near bifurcation points and plays important roles in enhancing information. The stochastic rhythms corresponding to Hopf bifurcation points with fixed firing frequency exhibited stronger coherence degree and a sharper peak in the power spectrum of the spike trains than those corresponding to saddle-node bifurcation points without fixed firing frequency. Moreover, the stochastic firing patterns changed to a depolarization resting state as the extracellular potassium concentration increased for the injured nerve fiber related to pathological pain or static blood pressure level increased for aortic depressor nerve fiber, and firing frequency decreased, which were different from the physiological viewpoint that firing frequency increased with increasing pressure level or potassium concentration. This shows that rhythms or firing patterns can reflect pressure or ion concentration information related to pathological pain information. Our results present the dynamics of stochastic firing patterns near bifurcation points, which are helpful for the identification of both dynamics and physiological roles of complex neural firing patterns or rhythms, and the roles of noise.

DROP TAIL AND RED QUEUE MANAGEMENT WITH SMALL BUFFERS:STABILITY AND HOPF BIFURCATION

Directory of Open Access Journals (Sweden)

Ganesh Patil

2011-06-01

Full Text Available There are many factors that are important in the design of queue management schemes for routers in the Internet: for example, queuing delay, link utilization, packet loss, energy consumption and the impact of router buffer size. By considering a fluid model for the congestion avoidance phase of Additive Increase Multiplicative Decrease (AIMD TCP, in a small buffer regime, we argue that stability should also be a desirable feature for network performance. The queue management schemes we study are Drop Tail and Random Early Detection (RED. For Drop Tail, the analytical arguments are based on local stability and bifurcation theory. As the buffer size acts as a bifurcation parameter, variations in it can readily lead to the emergence of limit cycles. We then present NS2 simulations to study the effect of changing buffer size on queue dynamics, utilization, window size and packet loss for three different flow scenarios. The simulations corroborate the analysis which highlights that performance is coupled with the notion of stability. Our work suggests that, in a small buffer regime, a simple Drop Tail queue management serves to enhance stability and appears preferable to the much studied RED scheme.

Bifurcation analysis of a delay differential equation model associated with the induction of long-term memory

International Nuclear Information System (INIS)

Hao, Lijie; Yang, Zhuoqin; Lei, Jinzhi

2015-01-01

Highlights: • A delay differentiation equation model for CREB regulation is developed. • Increasing the time delay can generate various bifurcations. • Increasing the time delay can induce chaos by two routes. - Abstract: The ability to form long-term memories is an important function for the nervous system, and the formation process is dynamically regulated through various transcription factors, including CREB proteins. In this paper, we investigate the dynamics of a delay differential equation model for CREB protein activities, which involves two positive and two negative feedbacks in the regulatory network. We discuss the dynamical mechanisms underlying the induction of long-term memory, in which bistability is essential for the formation of long-term memory, while long time delay can destabilize the high level steady state to inhibit the long-term memory formation. The model displays rich dynamical response to stimuli, including monostability, bistability, and oscillations, and can transit between different states by varying the negative feedback strength. Introduction of a time delay to the model can generate various bifurcations such as Hopf bifurcation, fold limit cycle bifurcation, Neimark–Sacker bifurcation of cycles, and period-doubling bifurcation, etc. Increasing the time delay can induce chaos by two routes: quasi-periodic route and period-doubling cascade.

Transition to magnetorotational turbulence in Taylor–Couette flow with imposed azimuthal magnetic field

International Nuclear Information System (INIS)

A Guseva; Avila, M; Willis, A P; Hollerbach, R

2015-01-01

The magnetorotational instability (MRI) is thought to be a powerful source of turbulence and momentum transport in astrophysical accretion discs, but obtaining observational evidence of its operation is challenging. Recently, laboratory experiments of Taylor–Couette flow with externally imposed axial and azimuthal magnetic fields have revealed the kinematic and dynamic properties of the MRI close to the instability onset. While good agreement was found with linear stability analyses, little is known about the transition to turbulence and transport properties of the MRI. We here report on a numerical investigation of the MRI with an imposed azimuthal magnetic field. We show that the laminar Taylor–Couette flow becomes unstable to a wave rotating in the azimuthal direction and standing in the axial direction via a supercritical Hopf bifurcation. Subsequently, the flow features a catastrophic transition to spatio-temporal defects which is mediated by a subcritical subharmonic Hopf bifurcation. Our results are in qualitative agreement with the PROMISE experiment and dramatically extend their realizable parameter range. We find that as the Reynolds number increases defects accumulate and grow into turbulence, yet the momentum transport scales weakly. (paper)

Hopf Algebroids and Their Cyclic Theory

NARCIS (Netherlands)

Kowalzig, N.

2009-01-01

The main objective of this thesis is to clarify concepts of generalised symmetries in noncommutative geometry (i.e., the noncommutative analogue of groupoids and Lie algebroids) and their associated (co)homologies. These ideas are incorporated by the notion of Hopf algebroids and Hopf-cyclic

Regularizations of two-fold bifurcations in planar piecewise smooth systems using blowup

DEFF Research Database (Denmark)

Kristiansen, Kristian Uldall; Hogan, S. J.

2015-01-01

type of limit cycle that does not appear to be present in the original PWS system. For both types of limit cycle, we show that the criticality of the Hopf bifurcation that gives rise to periodic orbits is strongly dependent on the precise form of the regularization. Finally, we analyse the limit cycles...... as locally unique families of periodic orbits of the regularization and connect them, when possible, to limit cycles of the PWS system. We illustrate our analysis with numerical simulations and show how the regularized system can undergo a canard explosion phenomenon...

Dynamical study of a chaotic predator-prey model with an omnivore

Science.gov (United States)

Al-khedhairi, A.; Elsadany, A. A.; Elsonbaty, A.; Abdelwahab, A. G.

2018-01-01

In this paper, the dynamics and bifurcations of a three-species predator-prey model with an omnivore are further investigated. The food web considered in this work comprises prey, predator and a third species, which consumes the carcasses of the predator along with predation of the original prey. The conditions for existence, uniqueness and continuous dependence on initial conditions for the solution of the model are derived. Analytical and numerical bifurcation studies reveal that the system undergoes transcritical and Hopf bifurcations around its equilibrium points. Further, the Hopf bifurcation curves in the parameters' space along with codimension two bifurcations of equilibrium points and bifurcation of limit cycles that arise in the system are investigated. In particular, the occurrence of generalized Hopf, fold Hopf and Neimarck-Sacker bifurcations is unveiled and illustrates the rich dynamics of the model. Finally, bifurcation diagrams, phase portraits and Lyapunov exponents of the model are presented.

Differential geometry on Hopf algebras and quantum groups

International Nuclear Information System (INIS)

Watts, P.

1994-01-01

The differential geometry on a Hopf algebra is constructed, by using the basic axioms of Hopf algebras and noncommutative differential geometry. The space of generalized derivations on a Hopf algebra of functions is presented via the smash product, and used to define and discuss quantum Lie algebras and their properties. The Cartan calculus of the exterior derivative, Lie derivative, and inner derivation is found for both the universal and general differential calculi of an arbitrary Hopf algebra, and, by restricting to the quasitriangular case and using the numerical R-matrix formalism, the aforementioned structures for quantum groups are determined

Hopf solitons in the Nicole model

International Nuclear Information System (INIS)

Gillard, Mike; Sutcliffe, Paul

2010-01-01

The Nicole model is a conformal field theory in a three-dimensional space. It has topological soliton solutions classified by the integer-valued Hopf charge, and all currently known solitons are axially symmetric. A volume-preserving flow is used to construct soliton solutions numerically for all Hopf charges from 1 to 8. It is found that the known axially symmetric solutions are unstable for Hopf charges greater than 2 and new lower energy solutions are obtained that include knots and links. A comparison with the Skyrme-Faddeev model suggests many universal features, though there are some differences in the link types obtained in the two theories.

Hopf algebras and topological recursion

International Nuclear Information System (INIS)

Esteves, João N

2015-01-01

We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293–309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347–452). (paper)

Wave propagation in the Lorenz-96 model

Directory of Open Access Journals (Sweden)

D. L. van Kekem

2018-04-01

Full Text Available In this paper we study the spatiotemporal properties of waves in the Lorenz-96 model and their dependence on the dimension parameter n and the forcing parameter F. For F > 0 the first bifurcation is either a supercritical Hopf or a double-Hopf bifurcation and the periodic attractor born at these bifurcations represents a traveling wave. Its spatial wave number increases linearly with n, but its period tends to a finite limit as n → ∞. For F < 0 and odd n, the first bifurcation is again a supercritical Hopf bifurcation, but in this case the period of the traveling wave also grows linearly with n. For F < 0 and even n, however, a Hopf bifurcation is preceded by either one or two pitchfork bifurcations, where the number of the latter bifurcations depends on whether n has remainder 2 or 0 upon division by 4. This bifurcation sequence leads to stationary waves and their spatiotemporal properties also depend on the remainder after dividing n by 4. Finally, we explain how the double-Hopf bifurcation can generate two or more stable waves with different spatiotemporal properties that coexist for the same parameter values n and F.

Normal forms of Hopf-zero singularity

International Nuclear Information System (INIS)

Gazor, Majid; Mokhtari, Fahimeh

2015-01-01

The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative–nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov–Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov–Takens singularities. Despite this, the normal form computations of Bogdanov–Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative–nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto–Sivashinsky equations to demonstrate the applicability of our results. (paper)

Normal forms of Hopf-zero singularity

Science.gov (United States)

Gazor, Majid; Mokhtari, Fahimeh

2015-01-01

The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the set of all volume-preserving conservative systems while the other is the maximal Lie algebra of nonconservative systems. This introduces a unique conservative-nonconservative decomposition for the normal form systems. There exists a Lie-subalgebra that is Lie-isomorphic to a large family of vector fields with Bogdanov-Takens singularity. This gives rise to a conclusion that the local dynamics of formal Hopf-zero singularities is well-understood by the study of Bogdanov-Takens singularities. Despite this, the normal form computations of Bogdanov-Takens and Hopf-zero singularities are independent. Thus, by assuming a quadratic nonzero condition, complete results on the simplest Hopf-zero normal forms are obtained in terms of the conservative-nonconservative decomposition. Some practical formulas are derived and the results implemented using Maple. The method has been applied on the Rössler and Kuramoto-Sivashinsky equations to demonstrate the applicability of our results.

Towards a classification of rational Hopf algebras

International Nuclear Information System (INIS)

Fuchs, J.; Ganchev, A.; Vecsernyes, P.

1994-02-01

Rational Hopf algebras, i.e. certain quasitriangular weak quasi-Hopf *-algebras, are expected to describe the quantum symmetry of rational field theories. In this paper methods are developed which allow for a classification of all rational Hopf algebras that are compatible with some prescribed set of fusion rules. The algebras are parametrized by the solutions of the square, pentagon and hexagon identities. As examples, we classify all solutions for fusion rules with not more than three sectors, as well as for the level three affine A 1 (1) fusion rules. We also establish several general properties of rational Hopf algebras and present a graphical description of the coassociator in terms of labelled tetrahedra. The latter construction allows to make contact with conformal field theory fusing matrices and with invariants of three-manifolds and topological lattice field theory. (orig.)

Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach

Science.gov (United States)

Lukierski, Jerzy; Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel; Woronowicz, Mariusz

2018-02-01

We consider new Abelian twists of Poincare algebra describing nonsymmetric generalization of the ones given in [1], which lead to the class of Lie-deformed quantum Minkowski spaces. We apply corresponding twist quantization in two ways: as generating quantum Poincare-Hopf algebra providing quantum Poincare symmetries, and by considering the quantization which provides Hopf algebroid describing class of quantum relativistic phase spaces with built-in quantum Poincare covariance. If we assume that Lorentz generators are orbital i.e. do not describe spin degrees of freedom, one can embed the considered generalized phase spaces into the ones describing the quantum-deformed Heisenberg algebras.

Neimark-Sacker bifurcations and evidence of chaos in a discrete dynamical model of walkers

International Nuclear Information System (INIS)

Rahman, Aminur; Blackmore, Denis

2016-01-01

Bouncing droplets on a vibrating fluid bath can exhibit wave-particle behavior, such as being propelled by interacting with its own wave field. These droplets seem to walk across the bath, and thus are dubbed walkers. Experiments have shown that walkers can exhibit exotic dynamical behavior indicative of chaos. While the integro-differential models developed for these systems agree well with the experiments, they are difficult to analyze mathematically. In recent years, simpler discrete dynamical models have been derived and studied numerically. The numerical simulations of these models show evidence of exotic dynamics such as period doubling bifurcations, Neimark–Sacker (N–S) bifurcations, and even chaos. For example, in [1], based on simulations Gilet conjectured the existence of a supercritical N-S bifurcation as the damping factor in his one- dimensional path model. We prove Gilet’s conjecture and more; in fact, both supercritical and subcritical (N-S) bifurcations are produced by separately varying the damping factor and wave-particle coupling for all eigenmode shapes. Then we compare our theoretical results with some previous and new numerical simulations, and find complete qualitative agreement. Furthermore, evidence of chaos is shown by numerically studying a global bifurcation.

Wave propagation in the Lorenz-96 model

Science.gov (United States)

van Kekem, Dirk L.; Sterk, Alef E.

2018-04-01

In this paper we study the spatiotemporal properties of waves in the Lorenz-96 model and their dependence on the dimension parameter n and the forcing parameter F. For F > 0 the first bifurcation is either a supercritical Hopf or a double-Hopf bifurcation and the periodic attractor born at these bifurcations represents a traveling wave. Its spatial wave number increases linearly with n, but its period tends to a finite limit as n → ∞. For F traveling wave also grows linearly with n. For F < 0 and even n, however, a Hopf bifurcation is preceded by either one or two pitchfork bifurcations, where the number of the latter bifurcations depends on whether n has remainder 2 or 0 upon division by 4. This bifurcation sequence leads to stationary waves and their spatiotemporal properties also depend on the remainder after dividing n by 4. Finally, we explain how the double-Hopf bifurcation can generate two or more stable waves with different spatiotemporal properties that coexist for the same parameter values n and F.

Coxeter groups and Hopf algebras

CERN Document Server

Aguiar, Marcelo

2011-01-01

An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary backgrou

Coherence resonance in low-density jets

Science.gov (United States)

Zhu, Yuanhang; Gupta, Vikrant; Li, Larry K. B.

2017-11-01

Coherence resonance is a phenomenon in which the response of a stable nonlinear system to noise exhibits a peak in coherence at an intermediate noise amplitude. We report the first experimental evidence of coherence resonance in a purely hydrodynamic system, a low-density jet whose variants can be found in many natural and engineering systems. This evidence comprises four parts: (i) the jet's response amplitude increases as the Reynolds number approaches the instability boundary under a constant noise amplitude; (ii) as the noise amplitude increases, the amplitude distribution of the jet response first becomes unimodal, then bimodal, and finally unimodal again; (iii) a distinct peak emerges in the coherence factor at an intermediate noise amplitude; and (iv) for a subcritical Hopf bifurcation, the decay rate of the autocorrelation function exhibits a maximum at an intermediate noise amplitude, but for a supercritical Hopf bifurcation, the decay rate decreases monotonically with increasing noise amplitude. It is clear that coherence resonance can provide valuable information about a system's nonlinearity even in the unconditionally stable regime, opening up new possibilities for its use in system identification and flow control. This work was supported by the Research Grants Council of Hong Kong (Project No. 16235716 and 26202815).

The Leibniz-Hopf algebra and Lyndon words

NARCIS (Netherlands)

M. Hazewinkel (Michiel)

1996-01-01

textabstractLet ${cal Z$ denote the free associative algebra ${ol Z langle Z_1 , Z_2 , ldots rangle$ over the integers. This algebra carries a Hopf algebra structure for which the comultiplication is $Z_n mapsto Sigma_{i+j=n Z_i otimes Z_j$. This the noncommutative Leibniz-Hopf algebra. It carries a

Generalized semilocal theories and higher Hopf maps

International Nuclear Information System (INIS)

Hindmarsh, M.; Holman, R.; Kephart, T.W.; Vachaspati, T.

1993-01-01

In semilocal theories, the vacuum manifold is fibered in a non-trivial way by the action of the gauge group. Here we generalize the original semilocal theory (which was based on the Hopf bundle S 3 → S1 S 2 ) to realize the next Hopf bundle S 7 →S 3 S 4 , and its extensions S 2n+1 → S3 HP n . The semilocal defects in this class of theories are classified by π 3 (S 3 ), and are interpreted as constrained instantons or generalized sphaleron configurations. We fail to find a field theoretic realization of the final Hopf bundle S 15 →S 7 S 8 , but are able to construct other semilocal spaces realizing Stiefel bundles over grassmannian spaces. (orig.)

Wigner oscillators, twisted Hopf algebras and second quantization

Energy Technology Data Exchange (ETDEWEB)

Castro, P.G.; Toppan, F. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mails: pgcastro@cbpf.br; toppan@cbpf.br; Chakraborty, B. [S. N. Bose National Center for Basic Sciences, Kolkata (India)]. E-mail: biswajit@bose.res.in

2008-07-01

By correctly identifying the role of central extension in the centrally extended Heisenberg algebra h, we show that it is indeed possible to construct a Hopf algebraic structure on the corresponding enveloping algebra U(h) and eventually deform it through Drinfeld twist. This Hopf algebraic structure and its deformed version U{sup F}(h) is shown to be induced from a more 'fundamental' Hopf algebra obtained from the Schroedinger field/oscillator algebra and its deformed version, provided that the fields/oscillators are regarded as odd-elements of a given superalgebra. We also discuss the possible implications in the context of quantum statistics. (author)

Poisson-Hopf limit of quantum algebras

International Nuclear Information System (INIS)

Ballesteros, A; Celeghini, E; Olmo, M A del

2009-01-01

The Poisson-Hopf analogue of an arbitrary quantum algebra U z (g) is constructed by introducing a one-parameter family of quantizations U z,ℎ (g) depending explicitly on ℎ and by taking the appropriate ℎ → 0 limit. The q-Poisson analogues of the su(2) algebra are discussed and the novel su q P (3) case is introduced. The q-Serre relations are also extended to the Poisson limit. This approach opens the perspective for possible applications of higher rank q-deformed Hopf algebras in semiclassical contexts

Transport Bifurcation in a Rotating Tokamak Plasma

International Nuclear Information System (INIS)

Highcock, E. G.; Barnes, M.; Schekochihin, A. A.; Parra, F. I.; Roach, C. M.; Cowley, S. C.

2010-01-01

The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all nonzero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients.

Subcritical thermal convection of liquid metals in a rapidly rotating sphere

Science.gov (United States)

Cardin, P.; Schaeffer, N.; Guervilly, C.; Kaplan, E.

2017-12-01

Planetary cores consist of liquid metals (low Prandtl number Pr) that convect as the core cools. Here we study nonlinear convection in a rotating (low Ekman number Ek) planetary core using a fully 3D direct (down to Ek=10-7) and a quasi geostrophic (down to Ek=10-10) numerical simulations. Near the critical thermal forcing (Rayleigh number Ra), convection onsets as thermal Rossby waves, but as Ra increases, this state is superceded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are continuously connected. As the planetary core rotates faster, the continuous transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at Ekforcing decreases well below the linear onset of convection (Ra 0.4Racrit in this study for Ek=10-10 and Pr=0.01). We highlight the importance of the Reynolds stress, which is required for convection to persist below the linear onset. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective subcritical state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for planetary interiors, thermal convection of liquid metals in a sphere onsets and shuts down through a subcritical bifurcation. This scenario may be relevant to explain the lunar and martian dynamo extinctions.

Bifurcation of Lane Change and Control on Highway for Tractor-Semitrailer under Rainy Weather

Directory of Open Access Journals (Sweden)

Tao Peng

2017-01-01

Full Text Available A new method is proposed for analyzing the nonlinear dynamics and stability in lane changes on highways for tractor-semitrailer under rainy weather. Unlike most of the literature associated with a simulated linear dynamic model for tractor-semitrailers steady steering on dry road, a verified 5DOF mechanical model with nonlinear tire based on vehicle test was used in the lane change simulation on low adhesion coefficient road. According to Jacobian matrix eigenvalues of the vehicle model, bifurcations of steady steering and sinusoidal steering on highways under rainy weather were investigated using a numerical method. Furthermore, based on feedback linearization theory, taking the tractor yaw rate and joint angle as control objects, a feedback linearization controller combined with AFS and DYC was established. The numerical simulation results reveal that Hopf bifurcations are identified in steady and sinusoidal steering conditions, which translate into an oscillatory behavior leading to instability. And simulations of urgent step and single-lane change in high velocity show that the designed controller has good effects on eliminating bifurcations and improving lateral stability of tractor-semitrailer, during lane changing on highway under rainy weather. It is a valuable reference for safety design of tractor-semitrailers to improve the traffic safety with driver-vehicle-road closed-loop system.

Accelerator driven sub-critical core

Science.gov (United States)

McIntyre, Peter M; Sattarov, Akhdiyor

2015-03-17

Systems and methods for operating an accelerator driven sub-critical core. In one embodiment, a fission power generator includes a sub-critical core and a plurality of proton beam generators. Each of the proton beam generators is configured to concurrently provide a proton beam into a different area of the sub-critical core. Each proton beam scatters neutrons within the sub-critical core. The plurality of proton beam generators provides aggregate power to the sub-critical core, via the proton beams, to scatter neutrons sufficient to initiate fission in the sub-critical core.

q-deformed conformal superalgebra and its Hopf subalgebras

International Nuclear Information System (INIS)

Dobrev, V.K.; Lukierski, J.; Sobczyk, J.; Tolstoy, V.N.

1992-07-01

We present in detail a Hopf superalgebra U q (su(2,2/2)) which is a q-deformation of the conformal superalgebra su(2,2/1). The superalgebra U q (su(2,2/1)) contains as a subalgebra a q-deformed super-Poincare algebra and as Hopf subalgebras two conjugate 16-generator q-deformed super-Weyl algebras, which are q-deformation of parabolic subalgebras of su(2,2/1). We use several (anti-) involutions, including the standard Cartan involution and a *-antiinvolution under which the super-Weyl algebras are *-subalgebras of U q (su(2,2/1)). The q-deformed Lorentz algebra is Hopf subalgebra of both Weyl algebras and is preserved by all (anti-) involutions considered. (author). 26 refs

Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

Directory of Open Access Journals (Sweden)

Hongwei Luo

2017-01-01

Full Text Available A PI hydroturbine governing system with saturation and double delays is generated in small perturbation. The nonlinear dynamic behavior of the system is investigated. More precisely, at first, we analyze the stability and Hopf bifurcation of the PI hydroturbine governing system with double delays under the four different cases. Corresponding stability theorem and Hopf bifurcation theorem of the system are obtained at equilibrium points. And then the stability of periodic solution and the direction of the Hopf bifurcation are illustrated by using the normal form method and center manifold theorem. We find out that the stability and direction of the Hopf bifurcation are determined by three parameters. The results have great realistic significance to guarantee the power system frequency stability and improve the stability of the hydropower system. At last, some numerical examples are given to verify the correctness of the theoretical results.

Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system

International Nuclear Information System (INIS)

Zhang Jiangang; Li Xianfeng; Chu Yandong; Yu Jianning; Chang Yingxiang

2009-01-01

In this paper, complex dynamical behavior of a class of centrifugal flywheel governor system is studied. These systems have a rich variety of nonlinear behavior, which are investigated here by numerically integrating the Lagrangian equations of motion. A tiny change in parameters can lead to an enormous difference in the long-term behavior of the system. Bubbles of periodic orbits may also occur within the bifurcation sequence. Hyperchaotic behavior is also observed in cases where two of the Lyapunov exponents are positive, one is zero, and one is negative. The routes to chaos are analyzed using Poincare maps, which are found to be more complicated than those of nonlinear rotational machines. Periodic and chaotic motions can be clearly distinguished by all of the analytical tools applied here, namely Poincare sections, bifurcation diagrams, Lyapunov exponents, and Lyapunov dimensions. This paper proposes a parametric open-plus-closed-loop approach to controlling chaos, which is capable of switching from chaotic motion to any desired periodic orbit. The theoretical work and numerical simulations of this paper can be extended to other systems. Finally, the results of this paper are of practical utility to designers of rotational machines.

Subcriticality determination of nuclear reactor

International Nuclear Information System (INIS)

Borisenko, V.I.; Goranchuk, V.V.; Sidoruk, N.M.; Volokh, A.F.

2014-01-01

In this article the subcriticality determination of nuclear reactor is considered. Emphasized that, despite the requirements of regulatory documents on the subcriticality determination of WWER from the beginning of their operation, so far, this problem has not been solved. The results of subcriticality determination of Rossi-α method of the WWER-M is presented. The possibility of subcriticality determination of WWER is considered. The possibility of subcriticality determination of Rossi-α method with time resolution is of about 100 microseconds is also considered. The possible reasons for the error in subcriticality determination of the reactor are indicated

Nonlinear dynamics of attractive magnetic bearings

Science.gov (United States)

Hebbale, K. V.; Taylor, D. L.

1987-01-01

The nonlinear dynamics of a ferromagnetic shaft suspended by the force of attraction of 1, 2, or 4 independent electromagnets is presented. Each model includes a state variable feedback controller which has been designed using the pole placement method. The constitutive relationships for the magnets are derived analytically from magnetic circuit theory, and the effects of induced eddy currents due to the rotation of the journal are included using Maxwell's field relations. A rotor suspended by four electro-magnets with closed loop feedback is shown to have nine equilibrium points within the bearing clearance space. As the rotor spin speed increases, the system is shown to pass through a Hopf bifurcation (a flutter instability). Using center manifold theory, this bifurcation can be shown to be of the subcritical type, indicating an unstable limit cycle below the critical speed. The bearing is very sensitive to initial conditions, and the equilibrium position is easily upset by transient excitation. The results are confirmed by numerical simulation.

Compact quantum group C*-algebras as Hopf algebras with approximate unit

International Nuclear Information System (INIS)

Do Ngoc Diep; Phung Ho Hai; Kuku, A.O.

1999-04-01

In this paper, we construct and study the representation theory of a Hopf C*-algebra with approximate unit, which constitutes quantum analogue of a compact group C*-algebra. The construction is done by first introducing a convolution-product on an arbitrary Hopf algebra H with integral, and then constructing the L 2 and C*-envelopes of H (with the new convolution-product) when H is a compact Hopf *-algebra. (author)

Nonlinear response of a forced van der Pol-Duffing oscillator at non-resonant bifurcations of codimension two

International Nuclear Information System (INIS)

Ji, J.C.; Zhang, N.

2009-01-01

Non-resonant bifurcations of codimension two may appear in the controlled van der Pol-Duffing oscillator when two critical time delays corresponding to a double Hopf bifurcation have the same value. With the aid of centre manifold theorem and the method of multiple scales, the non-resonant response and two types of primary resonances of the forced van der Pol-Duffing oscillator at non-resonant bifurcations of codimension two are investigated by studying the possible solutions and their stability of the four-dimensional ordinary differential equations on the centre manifold. It is shown that the non-resonant response of the forced oscillator may exhibit quasi-periodic motions on a two- or three-dimensional (2D or 3D) torus. The primary resonant responses admit single and mixed solutions and may exhibit periodic motions or quasi-periodic motions on a 2D torus. Illustrative examples are presented to interpret the dynamics of the controlled system in terms of two dummy unfolding parameters and exemplify the periodic and quasi-periodic motions. The analytical predictions are found to be in good agreement with the results of numerical integration of the original delay differential equation.

Dynamics of a delayed business cycle model with general investment function

International Nuclear Information System (INIS)

Riad, Driss; Hattaf, Khalid; Yousfi, Noura

2016-01-01

Highlights: • A delayed business cycle model is formulated and rigorously analyzed. • Well-posedness of the model and local stability of the economic equilibrium are determined. • Direction and stability of the Hopf bifurcation are investigated. • Global existence of bifurcating periodic solutions is established. • Numerical simulations are presented to illustrate our theoretical results. - Abstract: The aim of this paper is to study the dynamics of a delayed business cycle model with general investment function. The model describes the interaction of the gross product and capital stock. Furthermore, the delay represents the time between the decision of investment and implementation. Firstly, we show that the model is well posed by proving the global existence and boundedness of solutions. Secondly, we determine the economic equilibrium of the model. By analyzing the characteristic equation, we investigate the stability of the economic equilibrium and the local existence of Hopf bifurcation. Also, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theory. Moreover, the global existence of bifurcating periodic solutions is established by using the global Hopf bifurcation theory. Finally, our theoretical results are illustrated with some numerical simulations.

Complex nonlinear behaviour of a fixed bed reactor with reactant recycle

DEFF Research Database (Denmark)

Recke, Bodil; Jørgensen, Sten Bay

1999-01-01

The fixed bed reactor with reactant recycle investigated in this paper can exhibit periodic solutions. These solutions bifurcate from the steady state in a Hopf bifurcation. The Hopf bifurcation encountered at the lowest value of the inlet concentration turns the steady state unstable and marks......,that the dynamic behaviour of a fixed bed reactor with reactant recycle is much more complex than previously reported....

Dynamical analysis and simulation of a 2-dimensional disease model with convex incidence

Science.gov (United States)

Yu, Pei; Zhang, Wenjing; Wahl, Lindi M.

2016-08-01

In this paper, a previously developed 2-dimensional disease model is studied, which can be used for both epidemiologic modeling and in-host disease modeling. The main attention of this paper is focused on various dynamical behaviors of the system, including Hopf and generalized Hopf bifurcations which yield bistability and tristability, Bogdanov-Takens bifurcation, and homoclinic bifurcation. It is shown that the Bogdanov-Takens bifurcation and homoclinic bifurcation provide a new mechanism for generating disease recurrence, that is, cycles of remission and relapse such as the viral blips observed in HIV infection.

Bifurcation analysis of oscillating network model of pattern recognition in the rabbit olfactory bulb

Science.gov (United States)

Baird, Bill

1986-08-01

A neural network model describing pattern recognition in the rabbit olfactory bulb is analysed to explain the changes in neural activity observed experimentally during classical Pavlovian conditioning. EEG activity recorded from an 8×8 arry of 64 electrodes directly on the surface on the bulb shows distinct spatial patterns of oscillation that correspond to the animal's recognition of different conditioned odors and change with conditioning to new odors. The model may be considered a variant of Hopfield's model of continuous analog neural dynamics. Excitatory and inhibitory cell types in the bulb and the anatomical architecture of their connection requires a nonsymmetric coupling matrix. As the mean input level rises during each breath of the animal, the system bifurcates from homogenous equilibrium to a spatially patterned oscillation. The theory of multiple Hopf bifurcations is employed to find coupled equations for the amplitudes of these unstable oscillatory modes independent of frequency. This allows a view of stored periodic attractors as fixed points of a gradient vector field and thereby recovers the more familiar dynamical systems picture of associative memory.

Quasi Hopf quantum symmetry in quantum theory

International Nuclear Information System (INIS)

Mack, G.; Schomerus, V.

1991-05-01

In quantum theory, internal symmetries more general than groups are possible. We show that quasitriangular quasi Hopf algebras G * as introduced by Drinfeld permit a consistent formulation of a transformation law of states in the physical Hilbert space H, of invariance of the ground state, and of a transformation law of field operators which is consistent with local braid relations of field operators as proposed by Froehlich. All this remains true when Drinfelds axioms are suitably weakened in order to build in truncated tensor products. Conversely, all the axioms of a weak quasitriangular quasi Hopf algebra are motivated from what physics demands of a symmetry. Unitarity requires in addition that G * admits a * -operation with certain properties. Invariance properties of Greens functions follow from invariance of the ground state and covariance of field operators as usual. Covariant adjoints and covariant products of field operators can be defined. The R-matrix elements in the local braid relations are in general operators in H. They are determined by the symmetry up to a phase factor. Quantum group algebras like U q (sl 2 ) with vertical strokeqvertical stroke=1 are examples of symmetries with special properties. We show that a weak quasitriangular quasi Hopf algebra G * is canonically associated with U q (sl 2 ) if q P =-1. We argue that these weak quasi Hopf algebras are the true symmetries of minimal conformal models. Their dual algebras G ('functions on the group') are neither commutative nor associative. (orig.)

Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation

Science.gov (United States)

Steyn-Ross, Moira L.; Steyn-Ross, D. A.; Sleigh, J. W.

2013-04-01

Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1Hz) similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial) symmetry-breaking bifurcation that is modulated by a Hopf (temporal) instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural sleep and comment on the

Quantum walks, deformed relativity and Hopf algebra symmetries.

Science.gov (United States)

Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo

2016-05-28

We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras-the usual Poincaré and theκ-Poincaré algebras. © 2016 The Author(s).

BRAHMMA - accelerator driven subcritical facility

International Nuclear Information System (INIS)

Roy, Tushar; Shukla, Shefali; Shukla, M.; Ray, N.K.; Kashyap, Y.S.; Patel, T.; Gadkari, S.C.

2017-01-01

Accelerator Driven Subcritical systems are being studied worldwide for their potential in burning minor actinides and reducing long term radiotoxicity of spent nuclear fuels. In order to pursue the physics studies of Accelerator Driven Subcritical systems, a thermal subcritical assembly BRAHMMA (BeOReflectedAndHDPeModeratedMultiplying Assembly) has been developed at Purnima Labs, BARC. The facility consists of two major components: Subcritical core and Accelerator (DT/ DD Purnima Neutron Generator)

Probe Knots and Hopf Insulators with Ultracold Atoms

Science.gov (United States)

Deng, Dong-Ling; Wang, Sheng-Tao; Sun, Kai; Duan, L.-M.

2018-01-01

Knots and links are fascinating and intricate topological objects. Their influence spans from DNA and molecular chemistry to vortices in superfluid helium, defects in liquid crystals and cosmic strings in the early universe. Here we find that knotted structures also exist in a peculiar class of three-dimensional topological insulators—the Hopf insulators. In particular, we demonstrate that the momentum-space spin textures of Hopf insulators are twisted in a nontrivial way, which implies the presence of various knot and link structures. We further illustrate that the knots and nontrivial spin textures can be probed via standard time-of-flight images in cold atoms as preimage contours of spin orientations in stereographic coordinates. The extracted Hopf invariants, knots, and links are validated to be robust to typical experimental imperfections. Our work establishes the existence of knotted structures in Hopf insulators, which may have potential applications in spintronics and quantum information processing. D.L.D., S.T.W. and L.M.D. are supported by the ARL, the IARPA LogiQ program, and the AFOSR MURI program, and supported by Tsinghua University for their visits. K.S. acknowledges the support from NSF under Grant No. PHY1402971. D.L.D. is also supported by JQI-NSF-PFC and LPS-MPO-CMTC at the final stage of this paper.

The Hopf algebra structure of the character rings of classical groups

International Nuclear Information System (INIS)

Fauser, Bertfried; Jarvis, Peter D; King, Ronald C

2013-01-01

The character ring Char-GL of covariant irreducible tensor representations of the general linear group admits a Hopf algebra structure isomorphic to the Hopf algebra Symm-Λ of symmetric functions. Here we study the character rings Char-O and Char-Sp of the orthogonal and symplectic subgroups of the general linear group within the same framework of symmetric functions. We show that Char-O and Char-Sp also admit natural Hopf algebra structures that are isomorphic to that of Char-GL, and hence to Symm-Λ. The isomorphisms are determined explicitly, along with the specification of standard bases for Char-O and Char-Sp analogous to those used for Symm-Λ. A major structural change arising from the adoption of these bases is the introduction of new orthogonal and symplectic Schur–Hall scalar products. Significantly, the adjoint with respect to multiplication no longer coincides, as it does in the Char-GL case, with a Foulkes derivative or skew operation. The adjoint and Foulkes derivative now require separate definitions, and their properties are explored here in the orthogonal and symplectic cases. Moreover, the Hopf algebras Char-O and Char-Sp are not self-dual. The dual Hopf algebras Char-O * and Char-Sp are identified. Finally, the Hopf algebra of the universal rational character ring Char-GLrat of mixed irreducible tensor representations of the general linear group is introduced and its structure maps identified. (paper)

Bifurcation and phase diagram of turbulence constituted from three different scale-length modes

Energy Technology Data Exchange (ETDEWEB)

Itoh, S.-I.; Kitazawa, A.; Yagi, M. [Kyushu Univ., Research Inst. for Applied Mechanics, Kasuga, Fukuoka (Japan); Itoh, K. [National Inst. for Fusion Science, Toki, Gifu (Japan)

2002-04-01

Cases where three kinds of fluctuations having the different typical scale-lengths coexist are analyzed, and the statistical theory of strong turbulence in inhomogeneous plasmas is developed. Statistical nonlinear interactions between fluctuations are kept in the analysis as the renormalized drag, statistical noise and the averaged drive. The nonlinear interplay through them induces a quenching or suppressing effect, even if all the modes are unstable when they are analyzed independently. Variety in mode appearance takes place: one mode quenches the other two modes, or one mode is quenched by the other two modes, etc. The bifurcation of turbulence is analyzed and a phase diagram is drawn. Phase diagrams with cusp type catastrophe and butterfly type catastrophe are obtained. The subcritical bifurcation is possible to occur through the nonlinear interplay, even though each one is supercritical turbulence when analyzed independently. Analysis reveals that the nonlinear stability boundary (marginal point) and the amplitude of each mode may substantially shift from the conventional results of independent analyses. (author)

A dynamic IS-LM business cycle model with two time delays in capital accumulation equation

Science.gov (United States)

Zhou, Lujun; Li, Yaqiong

2009-06-01

In this paper, we analyze a augmented IS-LM business cycle model with the capital accumulation equation that two time delays are considered in investment processes according to Kalecki's idea. Applying stability switch criteria and Hopf bifurcation theory, we prove that time delays cause the equilibrium to lose or gain stability and Hopf bifurcation occurs.

Polarization of light and Hopf fibration

International Nuclear Information System (INIS)

Jurco, B.

1987-01-01

A set of polarization states of quasi-monochromatic light is described geometrically in terms of the Hopf fibration. Several associated alternative polarization parametrizations are given explicitly, including the Stokes parameters. (author). 8 refs

The complexity of an investment competition dynamical model with imperfect information in a security market

International Nuclear Information System (INIS)

Xin Baogui; Ma Junhai; Gao Qin

2009-01-01

We present a nonlinear discrete dynamical model of investment competition with imperfect information for N heterogeneous oligopolists in a security market. In this paper, our focus is on a given three-dimensional model which exhibits highly rich dynamical behaviors. Based on Wen's Hopf bifurcation criterion [Wen GL. Criterion to identify Hopf bifurcations in maps of arbitrary dimension. Phys Rev E 2005;72:026201-3; Wen GL, Xu DL, Han X. On creation of Hopf bifurcations in discrete-time nonlinear systems. Chaos 2002;12(2):350-5] and Kuznetsov's normal form theory [Kuznetsov YA. Elements of applied bifurcation theory. New York: Springer-Verlag; 1998. p. 125-37], we study the model's stability, criterion and direction of Neimark-Sacker bifurcation. Moreover, we numerically simulate a complexity evolution route: fixed point, closed invariant curve, double closed invariant curves, fourfold closed invariant curves, strange attractor, period-3 closed invariant curve, period-3 2-tours, period-4 closed invariant curve, period-4 2-tours.

Hopf algebra structures in particle physics

International Nuclear Information System (INIS)

Weinzierl, Stefan

2004-01-01

In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I give a basic introduction to these algebras and review some occurrences in particle physics. (orig.)

Assessment of oscillatory stability constrained available transfer capability

International Nuclear Information System (INIS)

Jain, T.; Singh, S.N.; Srivastava, S.C.

2009-01-01

This paper utilizes a bifurcation approach to compute oscillatory stability constrained available transfer capability (ATC) in an electricity market having bilateral as well as multilateral transactions. Oscillatory instability in non-linear systems can be related to Hopf bifurcation. At the Hopf bifurcation, one pair of the critical eigenvalues of the system Jacobian reaches imaginary axis. A new optimization formulation, including Hopf bifurcation conditions, has been developed in this paper to obtain the dynamic ATC. An oscillatory stability based contingency screening index, which takes into account the impact of transactions on severity of contingency, has been utilized to identify critical contingencies to be considered in determining ATC. The proposed method has been applied for dynamic ATC determination on a 39-bus New England system and a practical 75-bus Indian system considering composite static load as well as dynamic load models. (author)

An SIRS model with a nonlinear incidence rate

International Nuclear Information System (INIS)

Jin Yu; Wang, Wendi; Xiao Shiwu

2007-01-01

The global dynamics of an SIRS model with a nonlinear incidence rate is investigated. We establish a threshold for a disease to be extinct or endemic, analyze the existence and asymptotic stability of equilibria, and verify the existence of bistable states, i.e., a stable disease free equilibrium and a stable endemic equilibrium or a stable limit cycle. In particular, we find that the model admits stability switches as a parameter changes. We also investigate the backward bifurcation, the Hopf bifurcation and Bogdanov-Takens bifurcation and obtain the Hopf bifurcation criteria and Bogdanov-Takens bifurcation curves, which are important for making strategies for controlling a disease

Generalized exclusion and Hopf algebras

International Nuclear Information System (INIS)

Yildiz, A

2002-01-01

We propose a generalized oscillator algebra at the roots of unity with generalized exclusion and we investigate the braided Hopf structure. We find that there are two solutions: these are the generalized exclusions of the bosonic and fermionic types. We also discuss the covariance properties of these oscillators

Stochastic resonance induced by novel random transitions of motion of FitzHugh-Nagumo neuron model

International Nuclear Information System (INIS)

Zhang Guangjun; Xu Jianxue

2005-01-01

In contrast to the previous studies which have dealt with stochastic resonance induced by random transitions of system motion between two coexisting limit cycle attractors in the FitzHugh-Nagumo (FHN) neuron model after Hopf bifurcation and which have dealt with the phenomenon of stochastic resonance induced by external noise when the model with periodic input has only one attractor before Hopf bifurcation, in this paper we have focused our attention on stochastic resonance (SR) induced by a novel transition behavior, the transitions of motion of the model among one attractor on the left side of bifurcation point and two attractors on the right side of bifurcation point under the perturbation of noise. The results of research show: since one bifurcation of transition from one to two limit cycle attractors and the other bifurcation of transition from two to one limit cycle attractors occur in turn besides Hopf bifurcation, the novel transitions of motion of the model occur when bifurcation parameter is perturbed by weak internal noise; the bifurcation point of the model may stochastically slightly shift to the left or right when FHN neuron model is perturbed by external Gaussian distributed white noise, and then the novel transitions of system motion also occur under the perturbation of external noise; the novel transitions could induce SR alone, and when the novel transitions of motion of the model and the traditional transitions between two coexisting limit cycle attractors after bifurcation occur in the same process the SR also may occur with complicated behaviors types; the mechanism of SR induced by external noise when FHN neuron model with periodic input has only one attractor before Hopf bifurcation is related to this kind of novel transition mentioned above

A dynamic IS-LM model with delayed taxation revenues

International Nuclear Information System (INIS)

De Cesare, Luigi; Sportelli, Mario

2005-01-01

Some recent contributions to Economic Dynamics have shown a new interest for delay differential equations. In line with these approaches, we re-proposed the problem of the existence of a finite lag between the accrual and the payment of taxes in a framework where never this type of lag has been considered: the well known IS-LM model. The qualitative study of the system of functional (delay) differential equations shows that the finite lag may give rise to a wide variety of dynamic behaviours. Specifically, varying the length of the lag and applying the 'stability switch criteria', we prove that the equilibrium point may lose or gain its local stability, so that a sequence of alternated stability/instability regions can be observed if some conditions hold. An important scenario arising from the analysis is the existence of limit cycles generated by sub-critical and supercritical Hopf bifurcations. As numerical simulations confirm, if multiple cycles exist, the so called 'crater bifurcation' can also be detected. Economic considerations about a stylized policy analysis stand by qualitative and numerical results in the paper

Walking dynamics of the passive compass-gait model under OGY-based state-feedback control: Analysis of local bifurcations via the hybrid Poincaré map

International Nuclear Information System (INIS)

Gritli, Hassène; Belghith, Safya

2017-01-01

Highlights: • We study the passive walking dynamics of the compass-gait model under OGY-based state-feedback control. • We analyze local bifurcations via a hybrid Poincaré map. • We show exhibition of the super(sub)-critical flip bifurcation, the saddle-node(saddle) bifurcation and a saddle-flip bifurcation. • An analysis via a two-parameter bifurcation diagram is presented. • Some new hidden attractors in the controlled passive walking dynamics are displayed. - Abstract: In our previous work, we have analyzed the passive dynamic walking of the compass-gait biped model under the OGY-based state-feedback control using the impulsive hybrid nonlinear dynamics. Such study was carried out through bifurcation diagrams. It was shown that the controlled bipedal gait exhibits attractive nonlinear phenomena such as the cyclic-fold (saddle-node) bifurcation, the period-doubling (flip) bifurcation and chaos. Moreover, we revealed that, using the controlled continuous-time dynamics, we encountered a problem in finding, identifying and hence following branches of (un)stable solutions in order to characterize local bifurcations. The present paper solves such problem and then provides a further investigation of the controlled bipedal walking dynamics using the developed analytical expression of the controlled hybrid Poincaré map. Thus, we show that analysis via such Poincaré map allows to follow branches of both stable and unstable fixed points in bifurcation diagrams and hence to explore the complete dynamics of the controlled compass-gait biped model. We demonstrate the generation, other than the conventional local bifurcations in bipedal walking, i.e. the flip bifurcation and the saddle-node bifurcation, of a saddle-saddle bifurcation, a subcritical flip bifurcation and a new type of a local bifurcation, the saddle-flip bifurcation. In addition, to further understand the occurrence of the local bifurcations, we present an analysis with a two-parameter bifurcation

Dynamical Regimes and the Dynamo Bifurcation in Geodynamo Simulations

Science.gov (United States)

Petitdemange, L.

2017-12-01

We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core : in a rotating spherical shell with thermally driven motions with no-slip boundaries. Unlike previous studies on dynamo bifurcations, the control parameters have been varied significantly in order to deduce general tendencies. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition is replaced by a region of bistability for which dipolar and multipolar dynamos coexist. Such a result was also observed in models with free-slip boundaries in which the strong shear of geostrophic zonal flows can develop and gives rise to non-dipolar fields. We show that a similar process develops in no-slip models when viscous effects are reduced sufficiently.Close to the onset of convection (Rac), the axial dipole grows exponentially in the kinematic phase and saturation occurs by marginally changing the flow structure close to the dynamo threshold Rmc. The resulting bifurcation is then supercritical.In the range 3RacIf (Ra/Ra_c>10), important zonal flows develop in non-magnetic models with low viscosity. The field topology depends on the initial magnetic field. The dipolar branch has a subcritical behaviour whereas the multipolar branch is supercritical. By approaching more realistic parameters, the extension of this bistable regime increases (lower Rossby numbers). An hysteretic behaviour questions the common interpretation for geomagnetic reversals. Far above Rm_c$, the Lorentz force becomes dominant, as it is expected in planetary cores.

A generalized business cycle model with delays in gross product and capital stock

International Nuclear Information System (INIS)

Hattaf, Khalid; Riad, Driss; Yousfi, Noura

2017-01-01

Highlights: • A generalized business cycle model is proposed and rigorously analyzed. • Well-posedness of the model and local stability of the economic equilibrium are investigated. • Direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are determined. • A special case and some numerical simulations are presented. - Abstract: In this work, we propose a delayed business cycle model with general investment function. The time delays are introduced into gross product and capital stock, respectively. We first prove that the model is mathematically and economically well posed. In addition, the stability of the economic equilibrium and the existence of Hopf bifurcation are investigated. Our main results show that both time delays can cause the macro-economic system to fluctuate and the economic equilibrium to lose or gain its stability. Moreover, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by means of the normal form method and center manifold theory. Furthermore, the models and results presented in many previous studies are improved and generalized.

Differential Hopf algebra structures on the universal enveloping algebra ofa Lie algebra

NARCIS (Netherlands)

N.W. van den Hijligenberg; R. Martini

1995-01-01

textabstractWe discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra

Interacting Turing-Hopf Instabilities Drive Symmetry-Breaking Transitions in a Mean-Field Model of the Cortex: A Mechanism for the Slow Oscillation

Directory of Open Access Journals (Sweden)

Moira L. Steyn-Ross

2013-05-01

Full Text Available Electrical recordings of brain activity during the transition from wake to anesthetic coma show temporal and spectral alterations that are correlated with gross changes in the underlying brain state. Entry into anesthetic unconsciousness is signposted by the emergence of large, slow oscillations of electrical activity (≲1  Hz similar to the slow waves observed in natural sleep. Here we present a two-dimensional mean-field model of the cortex in which slow spatiotemporal oscillations arise spontaneously through a Turing (spatial symmetry-breaking bifurcation that is modulated by a Hopf (temporal instability. In our model, populations of neurons are densely interlinked by chemical synapses, and by interneuronal gap junctions represented as an inhibitory diffusive coupling. To demonstrate cortical behavior over a wide range of distinct brain states, we explore model dynamics in the vicinity of a general-anesthetic-induced transition from “wake” to “coma.” In this region, the system is poised at a codimension-2 point where competing Turing and Hopf instabilities coexist. We model anesthesia as a moderate reduction in inhibitory diffusion, paired with an increase in inhibitory postsynaptic response, producing a coma state that is characterized by emergent low-frequency oscillations whose dynamics is chaotic in time and space. The effect of long-range axonal white-matter connectivity is probed with the inclusion of a single idealized point-to-point connection. We find that the additional excitation from the long-range connection can provoke seizurelike bursts of cortical activity when inhibitory diffusion is weak, but has little impact on an active cortex. Our proposed dynamic mechanism for the origin of anesthetic slow waves complements—and contrasts with—conventional explanations that require cyclic modulation of ion-channel conductances. We postulate that a similar bifurcation mechanism might underpin the slow waves of natural

Integrable N dimensional systems on the Hopf algebra and q deformations

International Nuclear Information System (INIS)

Lisitsyn, Ya.V.; Shapovalov, A.V.

2000-01-01

The class of integrable classic and quantum systems on the Hopf algebra, describing the n of interacting particles, is plotted. The general structure of the integrable Hamiltonian system for the Hopf algebra A(g) of the Lee simple algebra g is obtained, wherefrom it follows, that motion integrals depend on the linear combinations k of the phase space coordinates. The q-deformation standard procedure is carried out and the corresponding integrable system is obtained. The general scheme is illustrated by the examples of the sl(2), sl(3) and o(3, 1) algebras. The exact solution is achieved for the N-dimensional Hamiltonian system quantum analog on the Hopf algebra A (sl(2)) through the method of noncommutative integration of linear differential equations [ru

Constructing Hopf bifurcation lines for the stability of nonlinear systems with two time delays

Science.gov (United States)

Nguimdo, Romain Modeste

2018-03-01

Although the plethora real-life systems modeled by nonlinear systems with two independent time delays, the algebraic expressions for determining the stability of their fixed points remain the Achilles' heel. Typically, the approach for studying the stability of delay systems consists in finding the bifurcation lines separating the stable and unstable parameter regions. This work deals with the parametric construction of algebraic expressions and their use for the determination of the stability boundaries of fixed points in nonlinear systems with two independent time delays. In particular, we concentrate on the cases for which the stability of the fixed points can be ascertained from a characteristic equation corresponding to that of scalar two-delay differential equations, one-component dual-delay feedback, or nonscalar differential equations with two delays for which the characteristic equation for the stability analysis can be reduced to that of a scalar case. Then, we apply our obtained algebraic expressions to identify either the parameter regions of stable microwaves generated by dual-delay optoelectronic oscillators or the regions of amplitude death in identical coupled oscillators.

Bifurcations in the response of a flexible rotor in squeeze-film dampers with retainer springs

International Nuclear Information System (INIS)

Inayat-Hussain, Jawaid I.

2009-01-01

Squeeze-film dampers are commonly used in conjunction with rolling-element or hydrodynamic bearings in rotating machinery. Although these dampers serve to provide additional damping to the rotor-bearing system, there have however been some cases of rotors mounted in these dampers exhibiting non-linear behaviour. In this paper a numerical study is undertaken to determine the effects of design parameters, i.e., gravity parameter, W, mass ratio, α, and stiffness ratio, K, on the bifurcations in the response of a flexible rotor mounted in squeeze-film dampers with retainer springs. The numerical simulations were undertaken for a range of speed parameter, Ω, between 0.1 and 5.0. Numerical results showed that increasing K causes the onset speed of bifurcation to increase, whilst an increase of α reduces the onset speed of bifurcation. For a specific combination of K and α values, the onset speed of bifurcation appeared to be independent of W. The instability of the rotor response at this onset speed was due to a saddle-node bifurcation for all the parameter values investigated in this work with the exception of the combination of α = 0.1 and K = 0.5, where a secondary Hopf bifurcation was observed. The speed range of non-synchronous response was seen to decrease with the increase of α; in fact non-synchronous rotor response was totally absent for α=0.4. With the exception of the case α = 0.1, the speed range of non-synchronous response was also seen to decrease with the increase of K. Multiple responses of the rotor were observed at certain values of Ω for various combinations of parameters W, α and K, where, depending on the values of the initial conditions the rotor response could be either synchronous or quasi-periodic. The numerical results presented in this work were obtained for an unbalance parameter, U, value of 0.1, which is considered as the upper end of the normal unbalance range of most practical rotor systems. These results provide some insights

Analysis of current-driven oscillatory dynamics of single-layer homoepitaxial islands on crystalline conducting substrates

Science.gov (United States)

Dasgupta, Dwaipayan; Kumar, Ashish; Maroudas, Dimitrios

2018-03-01

We report results of a systematic study on the complex oscillatory current-driven dynamics of single-layer homoepitaxial islands on crystalline substrate surfaces and the dependence of this driven dynamical behavior on important physical parameters, including island size, substrate surface orientation, and direction of externally applied electric field. The analysis is based on a nonlinear model of driven island edge morphological evolution that accounts for curvature-driven edge diffusion, edge electromigration, and edge diffusional anisotropy. Using a linear theory of island edge morphological stability, we calculate a critical island size at which the island's equilibrium edge shape becomes unstable, which sets a lower bound for the onset of time-periodic oscillatory dynamical response. Using direct dynamical simulations, we study the edge morphological dynamics of current-driven single-layer islands at larger-than-critical size, and determine the actual island size at which the migrating islands undergo a transition from steady to time-periodic asymptotic states through a subcritical Hopf bifurcation. At the highest symmetry of diffusional anisotropy examined, on {111} surfaces of face-centered cubic crystalline substrates, we find that more complex stable oscillatory states can be reached through period-doubling bifurcation at island sizes larger than those at the Hopf points. We characterize in detail the island morphology and dynamical response at the stable time-periodic asymptotic states, determine the range of stability of these oscillatory states terminated by island breakup, and explain the morphological features of the stable oscillating islands on the basis of linear stability theory.

Subcritical convection of liquid metals in a rotating sphere using a quasi-geostrophic model

Science.gov (United States)

Guervilly, Céline; Cardin, Philippe

2016-12-01

We study nonlinear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals ($Pr\\in[10^{-2},10^{-1}]$). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than $10^{-6}$, which is continuous at the onset (supercritical bifurcation) and consists of thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of $10^{-8}$. On the strong branch, the Reynolds number of the flow is greater than $10^3$, and a strong zonal flow with multiple jets develops, even close to the nonlinear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis ($Ek=10^{-6}$, $Pr=10^{-2}$). Nonlinear oscillations are observed near the onset of convection for $Ek=10^{-7}$ and $Pr=10^{-1}$.

Subcritical nuclear assembly

Energy Technology Data Exchange (ETDEWEB)

Vega C, H. R., E-mail: fermineutron@yahoo.com [Universidad Autonoma de Zacatecas, Unidad Academica de Estudios Nucleares, Cipres No. 10, Fracc. La Penuela, 98068 Zacatecas (Mexico)

2014-08-15

A Subcritical Nuclear Assembly is a device where the nuclear-fission chain reaction is initiated and maintained using an external neutron source. It is a valuable educational and research tool where in a safe way many reactor parameters can be measured. Here, we have used the Wigner-Seitz method in the six-factor formula to calculate the effective multiplication factor of a subcritical nuclear reactor Nuclear Chicago model 9000. This reactor has approximately 2500 kg of natural uranium heterogeneously distributed in slugs. The reactor uses a {sup 239}PuBe neutron source that is located in the center of an hexagonal array. Using Monte Carlo methods, with the MCNP5 code, a three-dimensional model of the subcritical reactor was designed to estimate the effective multiplication factor, the neutron spectra, the total and thermal neutron fluences along the radial and axial axis. With the neutron spectra in two locations outside the reactor the ambient dose equivalent were estimated. (Author)

Subcritical nuclear assembly

International Nuclear Information System (INIS)

Vega C, H. R.

2014-08-01

A Subcritical Nuclear Assembly is a device where the nuclear-fission chain reaction is initiated and maintained using an external neutron source. It is a valuable educational and research tool where in a safe way many reactor parameters can be measured. Here, we have used the Wigner-Seitz method in the six-factor formula to calculate the effective multiplication factor of a subcritical nuclear reactor Nuclear Chicago model 9000. This reactor has approximately 2500 kg of natural uranium heterogeneously distributed in slugs. The reactor uses a 239 PuBe neutron source that is located in the center of an hexagonal array. Using Monte Carlo methods, with the MCNP5 code, a three-dimensional model of the subcritical reactor was designed to estimate the effective multiplication factor, the neutron spectra, the total and thermal neutron fluences along the radial and axial axis. With the neutron spectra in two locations outside the reactor the ambient dose equivalent were estimated. (Author)

Feynman graphs and related Hopf algebras

International Nuclear Information System (INIS)

Duchamp, G H E; Blasiak, P; Horzela, A; Penson, K A; Solomon, A I

2006-01-01

In a recent series of communications we have shown that the reordering problem of bosons leads to certain combinatorial structures. These structures may be associated with a certain graphical description. In this paper, we show that there is a Hopf Algebra structure associated with this problem which is, in a certain sense, unique

A nonlinear deformed su(2) algebra with a two-color quasitriangular Hopf structure

International Nuclear Information System (INIS)

Bonatsos, D.; Daskaloyannis, C.; Kolokotronis, P.; Ludu, A.; Quesne, C.

1997-01-01

Nonlinear deformations of the enveloping algebra of su(2), involving two arbitrary functions of J 0 and generalizing the Witten algebra, were introduced some time ago by Delbecq and Quesne. In the present paper, the problem of endowing some of them with a Hopf algebraic structure is addressed by studying in detail a specific example, referred to as scr(A) q + (1). This algebra is shown to possess two series of (N+1)-dimensional unitary irreducible representations, where N=0,1,2,hor-ellipsis. To allow the coupling of any two such representations, a generalization of the standard Hopf axioms is proposed by proceeding in two steps. In the first one, a variant and extension of the deforming functional technique is introduced: variant because a map between two deformed algebras, su q (2) and scr(A) q + (1), is considered instead of a map between a Lie algebra and a deformed one, and extension because use is made of a two-valued functional, whose inverse is singular. As a result, the Hopf structure of su q (2) is carried over to scr(A) q + (1), thereby endowing the latter with a double Hopf structure. In the second step, the definition of the coproduct, counit, antipode, and scr(R)-matrix is extended so that the double Hopf algebra is enlarged into a new algebraic structure. The latter is referred to as a two-color quasitriangular Hopf algebra because the corresponding scr(R)-matrix is a solution of the colored Yang endash Baxter equation, where the open-quotes colorclose quotes parameters take two discrete values associated with the two series of finite-dimensional representations. copyright 1997 American Institute of Physics

Subcriticality monitoring method for reactor

International Nuclear Information System (INIS)

Ueda, Makoto.

1991-01-01

The present invention accurately monitors the reactor subcriticality and ensures the critical safety, irrespective of the presence or absence of artificial neutron sources. That is, when the subcriticality is monitored upon reactivity changing operation which causes reactivity change to the reactor during shutdown, neutron monitors are disposed at a plurality of monitoring positions. Then, neutron counting ratio before and after conducting the reactivity changing operation is determined. The subcriticality of the reactor is monitored by the ratio and the state of scattering of the ratio of neutron counting rate between each of the neutron monitors. With such procedures, signals of the neutron monitors are used, the characteristic that the change of the signals depend on the change of the neutron multiplication of the reactor core can be utilized whether artificial neutron sources (external neutron sources) are disposed or not. Accordingly, the subcriticality can be monitored more reliably. (I.S.)

Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

OpenAIRE

Luo, Hongwei; Zhang, Jiangang; Du, Wenju; Lu, Jiarong; An, Xinlei

2017-01-01

A PI hydroturbine governing system with saturation and double delays is generated in small perturbation. The nonlinear dynamic behavior of the system is investigated. More precisely, at first, we analyze the stability and Hopf bifurcation of the PI hydroturbine governing system with double delays under the four different cases. Corresponding stability theorem and Hopf bifurcation theorem of the system are obtained at equilibrium points. And then the stability of periodic solution and the dire...

Dynamics in a delayed-neural network

International Nuclear Information System (INIS)

Yuan Yuan

2007-01-01

In this paper, we consider a neural network of four identical neurons with time-delayed connections. Some parameter regions are given for global, local stability and synchronization using the theory of functional differential equations. The root distributions in the corresponding characteristic transcendental equation are analyzed, Pitchfork bifurcation, Hopf and equivariant Hopf bifurcations are investigated by revealing the center manifolds and normal forms. Numerical simulations are shown the agreements with the theoretical results

Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra

NARCIS (Netherlands)

van den Hijligenberg, N.W.; van den Hijligenberg, N.W.; Martini, Ruud

1995-01-01

We discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra structure of

Macdonald operators and homological invariants of the colored Hopf link

International Nuclear Information System (INIS)

Awata, Hidetoshi; Kanno, Hiroaki

2011-01-01

Using a power sum (boson) realization for the Macdonald operators, we investigate the Gukov, Iqbal, Kozcaz and Vafa (GIKV) proposal for the homological invariants of the colored Hopf link, which include Khovanov-Rozansky homology as a special case. We prove the polynomiality of the invariants obtained by GIKV's proposal for arbitrary representations. We derive a closed formula of the invariants of the colored Hopf link for antisymmetric representations. We argue that a little amendment of GIKV's proposal is required to make all the coefficients of the polynomial non-negative integers. (paper)

Twisted Acceleration-Enlarged Newton-Hooke Hopf Algebras

International Nuclear Information System (INIS)

Daszkiewicz, M.

2010-01-01

Ten Abelian twist deformations of acceleration-enlarged Newton-Hooke Hopf algebra are considered. The corresponding quantum space-times are derived as well. It is demonstrated that their contraction limit τ → ∞ leads to the new twisted acceleration-enlarged Galilei spaces. (author)

Unsteady behavior of a confined jet in a cavity at moderate Reynolds numbers

International Nuclear Information System (INIS)

Bouchet, G; Climent, E

2012-01-01

Self-sustained oscillations in the sinuous mode are observed when a jet impinges on a rigid surface. Confined jet instability is experimentally and numerically investigated here at moderate Reynolds numbers. When the Reynolds number is varied, the dynamic response of the jet is unusual in comparison with that of similar configurations (hole-tone, jet edge, etc). Modal transitions are clearly detected when the Reynolds number is varied. However, these transitions result in a reduction of the frequency, which means that the wavelength grows with Reynolds number. Moreover, the instability that sets in at low Reynolds number, as a subcritical Hopf bifurcation, disappears only 25% above the threshold. Then, the flow becomes steady again and symmetric. This atypical behavior is compared with our previous study on a submerged fountain (Bouchet et al 2002 Europhys. Lett. 59 826). (paper)

Beam Flutter and Energy Harvesting in Internal Flow

Science.gov (United States)

Tosi, Luis Phillipe; Colonius, Tim; Sherrit, Stewart; Lee, Hyeong Jae

2017-11-01

Aeroelastic flutter, largely studied for causing engineering failures, has more recently been used as a means of extracting energy from the flow. Particularly, flutter of a cantilever or an elastically mounted plate in a converging-diverging flow passage has shown promise as an energy harvesting concept for internal flow applications. The instability onset is observed as a function of throat velocity, internal wall geometry, fluid and structure material properties. To enable these devices, our work explores features of the fluid-structure coupled dynamics as a function of relevant nondimensional parameters. The flutter boundary is examined through stability analysis of a reduced order model, and corroborated with numerical simulations at low Reynolds number. Experiments for an energy harvester design are qualitatively compared to results from analytical and numerical work, suggesting a robust limit cycle ensues due to a subcritical Hopf bifurcation. Bosch Corporation.

Measurement of subcriticality by a pulsing α-method

International Nuclear Information System (INIS)

Jitarev, V.E.; Kachanov, V.M.; Kuzmin, A.N.

1999-01-01

The report presents results of a pulsing α-method [1] for determination of the WWER system subcriticality. The pulsing α-method permits to conduct measurements of system subcriticality in conditions of subcritical state and large neutron background. Therefore this method can be used for the control of a subcriticality of storehouses of a burn up nuclear fuel and stopped reactor. (Authors)

Differential Hopf algebra structures on the Universal Enveloping Algebra of a Lie Algebra

NARCIS (Netherlands)

van den Hijligenberg, N.W.; van den Hijligenberg, N.; Martini, Ruud

1995-01-01

We discuss a method to construct a De Rham complex (differential algebra) of Poincaré–Birkhoff–Witt type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebrastructure of U(g).

ENHANCED ELECTROCHEMICAL PROCESSES IN SUBCRITICAL WATER

Energy Technology Data Exchange (ETDEWEB)

Steven B. Hawthorne

2000-07-01

This project involved designing and performing preliminary electrochemical experiments in subcritical water. An electrochemical cell with substantially better performance characteristics than presently available was designed, built, and tested successfully. The electrochemical conductivity of subcritical water increased substantially with temperature, e.g., conductivities increased by a factor of 120 when the temperature was increased from 25 to 250 C. Cyclic voltammograms obtained with platinum and nickel demonstrated that the voltage required to produce hydrogen and oxygen from water can be dropped by a factor of three in subcritical water compared to the voltages required at ambient temperatures. However, no enhancement in the degradation of 1,2-dichlorobenzene and the polychlorinated biphenyl 3,3',4,4'-tetrachlorobiphenyl was observed with applied potential in subcritical water.

Benchmarking criticality safety calculations with subcritical experiments

International Nuclear Information System (INIS)

Mihalczo, J.T.

1984-06-01

Calculation of the neutron multiplication factor at delayed criticality may be necessary for benchmarking calculations but it may not be sufficient. The use of subcritical experiments to benchmark criticality safety calculations could result in substantial savings in fuel material costs for experiments. In some cases subcritical configurations could be used to benchmark calculations where sufficient fuel to achieve delayed criticality is not available. By performing a variety of measurements with subcritical configurations, much detailed information can be obtained which can be compared directly with calculations. This paper discusses several measurements that can be performed with subcritical assemblies and presents examples that include comparisons between calculation and experiment where possible. Where not, examples from critical experiments have been used but the measurement methods could also be used for subcritical experiments

Subcritical thermal convection of liquid metals in a rotating sphere using a quasi-geostrophic model

Science.gov (United States)

Cardin, P.; Guervilly, C.

2016-12-01

We study non-linear convection in a rapidly rotating sphere with internal heating for values of the Prandtl number relevant for liquid metals (10-2-1). We use a numerical model based on the quasi-geostrophic approximation, in which variations of the axial vorticity along the rotation axis are neglected, whereas the temperature field is fully three-dimensional. We identify two separate branches of convection close to onset: (i) a well-known weak branch for Ekman numbers greater than 10-6, which is continuous at the onset (supercritical bifurcation) and consists of the interaction of thermal Rossby waves, and (ii) a novel strong branch at lower Ekman numbers, which is discontinuous at the onset. The strong branch becomes subcritical for Ekman numbers of the order of 10-8. On the strong branch, the Reynolds number of the flow is greater than 1000, and a strong zonal flow with multiple jets develops, even close to the non-linear onset of convection. We find that the subcriticality is amplified by decreasing the Prandtl number. The two branches can co-exist for intermediate Ekman numbers, leading to hysteresis (E = 10-6, Pr =10-2). Non-linear oscillations are observed near the onset of convection for E = 10-7 and Pr = 10-1.

Generalized Cole–Hopf transformations for generalized Burgers ...

Indian Academy of Sciences (India)

2015-10-15

Oct 15, 2015 ... Cole–Hopf transformations; Burgers equation; invariance analysis. ... was to generate nonlinear parabolic equations from a linear parabolic equation via a ..... BMV acknowledges the financial support to attend the NMI Workshop ... [16] P J Olver, Applications of Lie Groups to differential equations, Graduate ...

The geometric Hopf invariant and surgery theory

CERN Document Server

Crabb, Michael

2017-01-01

Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. .

Relative Hom-Hopf modules and total integrals

International Nuclear Information System (INIS)

Guo, Shuangjian; Zhang, Xiaohui; Wang, Shengxiang

2015-01-01

Let (H, α) be a monoidal Hom-Hopf algebra and (A, β) a right (H, α)-Hom-comodule algebra. We first investigate the criterion for the existence of a total integral of (A, β) in the setting of monoidal Hom-Hopf algebras. Also, we prove that there exists a total integral ϕ : (H, α) → (A, β) if and only if any representation of the pair (H, A) is injective in a functorial way, as a corepresentation of (H, α), which generalizes Doi’s result. Finally, we define a total quantum integral γ : H → Hom(H, A) and prove the following affineness criterion: if there exists a total quantum integral γ and the canonical map ψ : A⊗ B A → A ⊗ H, a⊗ B b ↦ β −1 (a) b [0] ⊗ α(b [1] ) is surjective, then the induction functor A⊗ B −:ℋ ~ (ℳ k ) B →ℋ ~ (ℳ k ) A H is an equivalence of categories

Qualitative dynamical analysis of chaotic plasma perturbations model

Science.gov (United States)

Elsadany, A. A.; Elsonbaty, Amr; Agiza, H. N.

2018-06-01

In this work, an analytical framework to understand nonlinear dynamics of plasma perturbations model is introduced. In particular, we analyze the model presented by Constantinescu et al. [20] which consists of three coupled ODEs and contains three parameters. The basic dynamical properties of the system are first investigated by the ways of bifurcation diagrams, phase portraits and Lyapunov exponents. Then, the normal form technique and perturbation methods are applied so as to the different types of bifurcations that exist in the model are investigated. It is proved that pitcfork, Bogdanov-Takens, Andronov-Hopf bifurcations, degenerate Hopf and homoclinic bifurcation can occur in phase space of the model. Also, the model can exhibit quasiperiodicity and chaotic behavior. Numerical simulations confirm our theoretical analytical results.

Subcritical assemblies, use and their feasibility assessment

International Nuclear Information System (INIS)

Haroon, M.R.

1982-03-01

In developing countries, subcritical assemblies can be a useful tool for training and research in the field of nuclear technology with minimum cost. The historical development of subcritical assemblies and the reactor physics experiments which can be carried out using this facility are outlined. The different types of subcritical assemblies have been described and material requirements for each assembly have been pointed out. (author)

Design project of fast subcritical system 'Mala Lasta'

International Nuclear Information System (INIS)

Milosevic, M.; Stefanovic, D.; Popovic, D.; Pesic, M.; Zavaljevski, N.; Nikolic, D.; Arsenovic, M.

1988-10-01

This report contains two parts. Part one covers the objective and fundamental elements for the choice of fast subcritical system 'Mala Lasta', review of the existing fast subcritical assemblies, and a description of the available domestic computer codes applied for calculating neutron reactor parameters. Comparison of results obtained by these codes for a number of existing subcritical assemblies was used for the choice of the design project described in part two of this report. It contains detailed description of the operating parameters of the chosen subcritical system based on the obtained calculated parameters

Deep subcritical levels measurements dependents upon kinetic distortion factors

International Nuclear Information System (INIS)

Pan Shibiao; Li Xiang; Fu Guo'en; Huang Liyuan; Mu Keliang

2013-01-01

The measurement of deep subcritical levels, with the increase of subcriticality, showed that the results impact on the kinetic distortion effect, along with neutron flux strongly deteriorated. Using the diffusion theory, calculations have been carried out to quantify the kinetic distortion correction factors in subcritical systems, and these indicate that epithermal neutron distributions are strongly affected by kinetic distortion. Subcriticality measurements in four different rod-state combination at the zero power device was carried out. The test data analysis shows that, with increasing subcriticality, kinetic distortion effect correction factor gradually increases from 1.052 to 1.065, corresponding reactive correction amount of 0.78β eff ∼ 3.01β eff . Thus, it is necessary to consider the kinetic distortion effect in the deep subcritical reactivity measurements. (authors)

Relative Hom-Hopf modules and total integrals

Energy Technology Data Exchange (ETDEWEB)

Guo, Shuangjian [School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025 (China); Zhang, Xiaohui [Department of Mathematics, Southeast University, Nanjing 210096 (China); Wang, Shengxiang, E-mail: wangsx-math@163.com [School of Mathematics and Finance, Chuzhou University, Chuzhou 239000 (China); Department of Mathematics, Nanjing University, Nanjing 210093 (China)

2015-02-15

Let (H, α) be a monoidal Hom-Hopf algebra and (A, β) a right (H, α)-Hom-comodule algebra. We first investigate the criterion for the existence of a total integral of (A, β) in the setting of monoidal Hom-Hopf algebras. Also, we prove that there exists a total integral ϕ : (H, α) → (A, β) if and only if any representation of the pair (H, A) is injective in a functorial way, as a corepresentation of (H, α), which generalizes Doi’s result. Finally, we define a total quantum integral γ : H → Hom(H, A) and prove the following affineness criterion: if there exists a total quantum integral γ and the canonical map ψ : A⊗{sub B}A → A ⊗ H, a⊗{sub B}b ↦ β{sup −1}(a) b{sub [0]} ⊗ α(b{sub [1]}) is surjective, then the induction functor A⊗{sub B}−:ℋ{sup ~}(ℳ{sub k}){sub B}→ℋ{sup ~}(ℳ{sub k}){sub A}{sup H} is an equivalence of categories.

Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories

International Nuclear Information System (INIS)

Sasai, Yuya; Sasakura, Naoki

2008-01-01

Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar φ 4 braided noncommutative field theory in Lie-algebraic noncommutative space-time, [x i ,x j ]=2iκε ijk x k (i,j,k=1,2,3), which has a Hopf algebraic translational symmetry. We first discuss the existence of a domain wall soliton in view of Derrick's theorem, and construct explicitly a one-parameter family of solutions in perturbation of the noncommutativity parameter κ. We then find the massless moduli field which propagates on the domain wall soliton. We further extend our analysis to the general Hopf algebraic translational symmetry

Dynamics of a Computer Virus Propagation Model with Delays and Graded Infection Rate

Directory of Open Access Journals (Sweden)

Zizhen Zhang

2017-01-01

Full Text Available A four-compartment computer virus propagation model with two delays and graded infection rate is investigated in this paper. The critical values where a Hopf bifurcation occurs are obtained by analyzing the distribution of eigenvalues of the corresponding characteristic equation. In succession, direction and stability of the Hopf bifurcation when the two delays are not equal are determined by using normal form theory and center manifold theorem. Finally, some numerical simulations are also carried out to justify the obtained theoretical results.

Nonfamilial acrokeratosis verruciformis of Hopf

Directory of Open Access Journals (Sweden)

Nidhi Patel

2015-01-01

Full Text Available Acrokeratosis verruciformis (AKV of Hopf is an autosomal dominant genodermatosis with unknown etiology. It is characterized by multiple flat-topped keratotic papules resembling planar warts located mainly on the dorsum of hands and feet. Superficial ablation is the treatment of choice. A 41-year-old female presented with multiple hyperpigmented, hyperkeratotic papules and plaques over flexor aspect of both forearms, extensors of both legs and dorsum of the feet. Histopathology showed changes of AKV. Patient was treated with a combination of topical corticosteroids and cryotherapy with no visible improvement.

Steady squares and hexagons on a subcritical ramp

International Nuclear Information System (INIS)

Hoyle, R.B.

1995-01-01

Steady squares and hexagons on a subcritical ramp are studied, both analytically and numerically, within the framework of the lowest-order amplitude equations. On the subcritical ramp, the external stress or control parameter varies continuously in space from subcritical to supercritical values. At the subcritical end of the ramp, pattern formation is suppressed, and patterns fade away into the conduction solution. It is shown that three-dimensional patterns may change shape on a subcritical ramp. A square pattern becomes a pattern of rolls as it fades, with the roll axes aligned in the direction orthogonal to that in which the control parameter varies. Hexagons in systems with horizontal midplane symmetry become a pattern of rectangles before reaching the conduction solution. There is a suggestion that hexagons in systems which lack this symmetry might fade away through a roll pattern. Numerical simulations are used to illustrate these phenomena

Large subcriticality measurement by pulsed neutron method

International Nuclear Information System (INIS)

Yamane, Y.; Yoshida, A.; Nishina, K.; Kobayashi, K.; Kanda, K.

1985-01-01

To establish the method determining large subcriticalities in the field of nuclear criticality safety, the authors performed pulsed neutron experiments using the Kyoto University Critical Assembly (KUCA) at Research Reactor Institute, Kyoto University and the Cockcroft-Walton type accelerator attached to the assembly. The area-ratio method proposed by Sjoestrand was employed to evaluate subcriticalities from neutron decay curves measured. This method has the shortcomings that the neutron component due to a decay of delayed neutrons remarkably decreases as the subcriticality of an objective increases. To overcome the shortcoming, the authors increased the frequency of pulsed neutron generation. The integral-version of the area-ratio method proposed by Kosaly and Fisher was employed in addition in order to remove a contamination of spatial higher modes from the decay curve. The latter becomes significant as subcriticality increases. The largest subcriticality determined in the present experiments was 125.4 dollars, which was equal to 0.5111 in a multiplication factor. The calculational values evaluated by the computer code KENO-IV with 137 energy groups based on the Monte Carlo method agreed well with those experimental values

Nonlinear modeling and stability analysis of hydro-turbine governing system with sloping ceiling tailrace tunnel under load disturbance

International Nuclear Information System (INIS)

Guo, Wencheng; Yang, Jiandong; Wang, Mingjiang; Lai, Xu

2015-01-01

Highlights: • Novel nonlinear mathematical model of hydro-turbine governing system is proposed. • Hopf bifurcation analysis on the governing system is conducted. • Stability of the system under load disturbance is studied. • Influence of four factors on stability is analyzed. • Optimization methods of improving system stability are put forward. - Abstract: In order to overcome the problem of nonlinear dynamics of hydro-turbine governing system with sloping ceiling tailrace tunnel, which is caused by the interface movement of the free surface-pressurized flow in the tailrace tunnel, and the difficulty of analyzing the stability of system, this paper uses the Hopf bifurcation theory to study the stability of hydro-turbine governing system of hydropower station with sloping ceiling tailrace tunnel. Firstly, a novel and rational nonlinear mathematical model of the hydro-turbine governing system is proposed. This model contains the dynamic equation of pipeline system which can accurately describe the motion characteristics of the interface of free surface-pressurized flow in sloping ceiling tailrace tunnel. According to the nonlinear mathematical model, the existence and direction of Hopf bifurcation of the nonlinear dynamic system are analyzed. Furthermore, the algebraic criterion of the occurrence of Hopf bifurcation is derived. Then the stability domain and bifurcation diagram of hydro-turbine governing system are drawn by the algebraic criterion, and the characteristics of stability under different state parameters are investigated. Finally, the influence of step load value, ceiling slope angle and section form of tailrace tunnel and water depth at the interface in tailrace tunnel on stability are analyzed based on stable domain. The results indicate that: The Hopf bifurcation of hydro-turbine governing system with sloping ceiling tailrace tunnel is supercritical. The phase space trajectories of characteristic variables stabilize at the equilibrium points

Unfolding the Riddling Bifurcation

DEFF Research Database (Denmark)

Maistrenko, Yu.; Popovych, O.; Mosekilde, Erik

1999-01-01

We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation.......We present analytical conditions for the riddling bifurcation in a system of two symmetrically coupled, identical, smooth one-dimensional maps to be soft or hard and describe a generic scenario for the transformations of the basin of attraction following a soft riddling bifurcation....

Bifurcation of synchronous oscillations into torus in a system of two reciprocally inhibitory silicon neurons: Experimental observation and modeling

International Nuclear Information System (INIS)

Bondarenko, Vladimir E.; Cymbalyuk, Gennady S.; Patel, Girish; DeWeerth, Stephen P.; Calabrese, Ronald L.

2004-01-01

Oscillatory activity in the central nervous system is associated with various functions, like motor control, memory formation, binding, and attention. Quasiperiodic oscillations are rarely discussed in the neurophysiological literature yet they may play a role in the nervous system both during normal function and disease. Here we use a physical system and a model to explore scenarios for how quasiperiodic oscillations might arise in neuronal networks. An oscillatory system of two mutually inhibitory neuronal units is a ubiquitous network module found in nervous systems and is called a half-center oscillator. Previously we created a half-center oscillator of two identical oscillatory silicon (analog Very Large Scale Integration) neurons and developed a mathematical model describing its dynamics. In the mathematical model, we have shown that an in-phase limit cycle becomes unstable through a subcritical torus bifurcation. However, the existence of this torus bifurcation in experimental silicon two-neuron system was not rigorously demonstrated or investigated. Here we demonstrate the torus predicted by the model for the silicon implementation of a half-center oscillator using complex time series analysis, including bifurcation diagrams, mapping techniques, correlation functions, amplitude spectra, and correlation dimensions, and we investigate how the properties of the quasiperiodic oscillations depend on the strengths of coupling between the silicon neurons. The potential advantages and disadvantages of quasiperiodic oscillations (torus) for biological neural systems and artificial neural networks are discussed

Sub-criticality monitoring for ADTR trademark control

International Nuclear Information System (INIS)

Ashworth, Roger

2014-01-01

Following the debut of the Accelerator Driven Thorium Reactor (ADTR trademark) Power Station at ENC 2010 in Barcelona, thorium as a reactor fuel has gained increasing support. The ADTR trademark concept reactor introduced the combination of an accelerator driven system (ADS) with traditional control rod technology, to provide a very high gain novel sub-critical ADS reactor design. The high gain of the system, while significantly reducing the demands on the accelerator design, pushes up operational sub-criticality (k eff ) closer to unity. In this paper we review this design and the progress made since ENC 2010. We compare 2 different methods of measuring the sub-critical neutron multiplication factor as the fuel cycle develops. The paper discusses the most recent work on k eff measurement and the interesting relationship between neutron flux, accelerator current and fuel temperature when using beam pulse methods to determine operational sub-criticality, of which a European patent is being granted. (orig.)

Wiener-Hopf operators on spaces of functions on R+ with values in a Hilbert space

OpenAIRE

Petkova, Violeta

2006-01-01

A Wiener-Hopf operator on a Banach space of functions on R+ is a bounded operator T such that P^+S_{-a}TS_a=T, for every positive a, where S_a is the operator of translation by a. We obtain a representation theorem for the Wiener-Hopf operators on a large class of functions on R+ with values in a separable Hilbert space.

La factorización de una transformada de Fourier en el método de Wiener-Hopf

OpenAIRE

José Rosales-Ortega; Carlos Márquez Rivera

2009-01-01

Using the Wiener-Hopf method, we factorize the Fourier Transform of the kernel of a singular integral equation as the product of two functions: one holomorphic in the upper semiplan and the other holomophic in the lower semiplan. Keywords: function product, Fourier transform, Wiener-Hopf method.

Dynamics of the congestion control model in underwater wireless sensor networks with time delay

International Nuclear Information System (INIS)

Dong, Tao; Hu, Wenjie; Liao, Xiaofeng

2016-01-01

In this paper, a congestion control model in underwater wireless sensor network with time delay is considered. First, the boundedness of the positive equilibrium, where the samples density is positive for each node and the different event flows coexist, is investigated, which implies that the samples density of sensor node cannot exceed the Environmental carrying capacity. Then, by considering the time delay can be regarded as a bifurcating parameter, the dynamical behaviors, which include local stability and Hopf bifurcation, are investigated. It is found that when the communication time delay passes a critical value, the system loses its stability and a Hopf bifurcation occurs, which means the underwater wireless sensor network will be congested, even collapsed. Furthermore, the direction and stability of the bifurcating periodic solutions are derived by applying the normal form theory and the center manifold theorem. Finally, some numerical examples are finally performed to verify the theoretical results.

Bifurcations sights, sounds, and mathematics

CERN Document Server

Matsumoto, Takashi; Kokubu, Hiroshi; Tokunaga, Ryuji

1993-01-01

Bifurcation originally meant "splitting into two parts. " Namely, a system under­ goes a bifurcation when there is a qualitative change in the behavior of the sys­ tem. Bifurcation in the context of dynamical systems, where the time evolution of systems are involved, has been the subject of research for many scientists and engineers for the past hundred years simply because bifurcations are interesting. A very good way of understanding bifurcations would be to see them first and study theories second. Another way would be to first comprehend the basic concepts and theories and then see what they look like. In any event, it is best to both observe experiments and understand the theories of bifurcations. This book attempts to provide a general audience with both avenues toward understanding bifurcations. Specifically, (1) A variety of concrete experimental results obtained from electronic circuits are given in Chapter 1. All the circuits are very simple, which is crucial in any experiment. The circuits, howev...

La factorización de una transformada de Fourier en el método de Wiener-Hopf

Directory of Open Access Journals (Sweden)

José Rosales-Ortega

2009-02-01

Full Text Available Using the Wiener-Hopf method, we factorize the Fourier Transform of the kernel of a singular integral equation as the product of two functions: one holomorphic in the upper semiplan and the other holomophic in the lower semiplan. Keywords: function product, Fourier transform, Wiener-Hopf method.

From racks to pointed Hopf algebras

OpenAIRE

Andruskiewitsch, Nicolás; Graña, Matı́as

2003-01-01

A fundamental step in the classification of finite-dimensional complex pointed Hopf algebras is the determination of all finite-dimensional Nichols algebras of braided vector spaces arising from groups. The most important class of braided vector spaces arising from groups is the class of braided vector spaces (CX, c^q), where C is the field of complex numbers, X is a rack and q is a 2-cocycle on X with values in C^*. Racks and cohomology of racks appeared also in the work of topologists. This...

Stability analysis of BWR nuclear-coupled thermal-hyraulics using a simple model

Energy Technology Data Exchange (ETDEWEB)

Karve, A.A.; Rizwan-uddin; Dorning, J.J. [Univ. of Virginia, Charlottesville, VA (United States)

1995-09-01

A simple mathematical model is developed to describe the dynamics of the nuclear-coupled thermal-hydraulics in a boiling water reactor (BWR) core. The model, which incorporates the essential features of neutron kinetics, and single-phase and two-phase thermal-hydraulics, leads to simple dynamical system comprised of a set of nonlinear ordinary differential equations (ODEs). The stability boundary is determined and plotted in the inlet-subcooling-number (enthalpy)/external-reactivity operating parameter plane. The eigenvalues of the Jacobian matrix of the dynamical system also are calculated at various steady-states (fixed points); the results are consistent with those of the direct stability analysis and indicate that a Hopf bifurcation occurs as the stability boundary in the operating parameter plane is crossed. Numerical simulations of the time-dependent, nonlinear ODEs are carried out for selected points in the operating parameter plane to obtain the actual damped and growing oscillations in the neutron number density, the channel inlet flow velocity, and the other phase variables. These indicate that the Hopf bifurcation is subcritical, hence, density wave oscillations with growing amplitude could result from a finite perturbation of the system even where the steady-state is stable. The power-flow map, frequently used by reactor operators during start-up and shut-down operation of a BWR, is mapped to the inlet-subcooling-number/neutron-density (operating-parameter/phase-variable) plane, and then related to the stability boundaries for different fixed inlet velocities corresponding to selected points on the flow-control line. The stability boundaries for different fixed inlet subcooling numbers corresponding to those selected points, are plotted in the neutron-density/inlet-velocity phase variable plane and then the points on the flow-control line are related to their respective stability boundaries in this plane.

Global existence of periodic solutions on a simplified BAM neural network model with delays

International Nuclear Information System (INIS)

Zheng Baodong; Zhang Yazhuo; Zhang Chunrui

2008-01-01

A simplified n-dimensional BAM neural network model with delays is considered. Some results of Hopf bifurcations occurring at the zero equilibrium as the delay increases are exhibited. Global existence of periodic solutions are established using a global Hopf bifurcation result of Wu [Wu J. Symmetric functional-differential equations and neural networks with memory. Trans Am Math Soc 1998;350:4799-838], and a Bendixson criterion for higher dimensional ordinary differential equations due to Li and Muldowney [Li MY, Muldowney J. On Bendixson's criterion. J Differ Equations 1994;106:27-39]. Finally, computer simulations are performed to illustrate the analytical results found

Dynamics analysis of a predator-prey system with harvesting prey and disease in prey species.

Science.gov (United States)

Meng, Xin-You; Qin, Ni-Ni; Huo, Hai-Feng

2018-12-01

In this paper, a predator-prey system with harvesting prey and disease in prey species is given. In the absence of time delay, the existence and stability of all equilibria are investigated. In the presence of time delay, some sufficient conditions of the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analysing the corresponding characteristic equation, and the properties of Hopf bifurcation are given by using the normal form theory and centre manifold theorem. Furthermore, an optimal harvesting policy is investigated by applying the Pontryagin's Maximum Principle. Numerical simulations are performed to support our analytic results.

Quantitative angiography methods for bifurcation lesions

DEFF Research Database (Denmark)

Collet, Carlos; Onuma, Yoshinobu; Cavalcante, Rafael

2017-01-01

Bifurcation lesions represent one of the most challenging lesion subsets in interventional cardiology. The European Bifurcation Club (EBC) is an academic consortium whose goal has been to assess and recommend the appropriate strategies to manage bifurcation lesions. The quantitative coronary...... angiography (QCA) methods for the evaluation of bifurcation lesions have been subject to extensive research. Single-vessel QCA has been shown to be inaccurate for the assessment of bifurcation lesion dimensions. For this reason, dedicated bifurcation software has been developed and validated. These software...

Simple or Complex Stenting for Bifurcation Coronary Lesions: A Patient-Level Pooled-Analysis of the Nordic Bifurcation Study and the British Bifurcation Coronary Study

DEFF Research Database (Denmark)

Behan, Miles W; Holm, Niels Ramsing; Curzen, Nicholas P

2011-01-01

Background— Controversy persists regarding the correct strategy for bifurcation lesions. Therefore, we combined the patient-level data from 2 large trials with similar methodology: the NORDIC Bifurcation Study (NORDIC I) and the British Bifurcation Coronary Study (BBC ONE). Methods and Results— B...

Cup products in Hopf cyclic cohomology with coefficients in contramodules

OpenAIRE

Rangipour, Bahram

2010-01-01

We use stable anti Yetter-Drinfeld contramodules to improve the cup products in Hopf cyclic cohomology. The improvement fixes the lack of functoriality of the cup products previously defined and show that the cup products are sensitive to the coefficients.

Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect

Directory of Open Access Journals (Sweden)

Wenjie Hu

2018-01-01

Full Text Available The dynamics behaviors of Kaldor–Kalecki business cycle model with diffusion effect and time delay under the Neumann boundary conditions are investigated. First the conditions of time-independent and time-dependent stability are investigated. Then, we find that the time delay can give rise to the Hopf bifurcation when the time delay passes a critical value. Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which can determine the bifurcation direction and the stability of the periodic solutions. Finally, numerical results not only validate the obtained theorems, but also show that the diffusion coefficients play a key role in the spatial pattern. With the diffusion coefficients increasing, different patterns appear.

Stability switches, oscillatory multistability, and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks.

Science.gov (United States)

Song, Yongli; Makarov, Valeri A; Velarde, Manuel G

2009-08-01

A model of time-delay recurrently coupled spatially segregated neural assemblies is here proposed. We show that it operates like some of the hierarchical architectures of the brain. Each assembly is a neural network with no delay in the local couplings between the units. The delay appears in the long range feedforward and feedback inter-assemblies communications. Bifurcation analysis of a simple four-units system in the autonomous case shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multistability, hysteresis, and stability switches of the rest state provoked by the time delay. Then we investigate the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric local Hopf bifurcation theory of delay differential equations and derive the equation describing the flow on the center manifold that enables us determining the direction of Hopf bifurcations and stability of the bifurcating periodic orbits. We also discuss computational properties of the system due to the delay when an external drive of the network mimicks external sensory input.

Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: Border-collision bifurcation curves

International Nuclear Information System (INIS)

Sushko, Iryna; Agliari, Anna; Gardini, Laura

2006-01-01

We study the structure of the 2D bifurcation diagram for a two-parameter family of piecewise smooth unimodal maps f with one break point. Analysing the parameters of the normal form for the border-collision bifurcation of an attracting n-cycle of the map f, we describe the possible kinds of dynamics associated with such a bifurcation. Emergence and role of border-collision bifurcation curves in the 2D bifurcation plane are studied. Particular attention is paid also to the curves of homoclinic bifurcations giving rise to the band merging of pieces of cyclic chaotic intervals

Relative Lyapunov Center Bifurcations

DEFF Research Database (Denmark)

Wulff, Claudia; Schilder, Frank

2014-01-01

Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...... center theorem of Montaldi, Roberts, and Stewart. We then develop numerical methods for the detection of relative Lyapunov center bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian REs of the N-body problem....

Hopf structure and Green ansatz of deformed parastatistics algebras

Energy Technology Data Exchange (ETDEWEB)

Aneva, Boyka [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, bld. Tsarigradsko chaussee 72, BG-1784 Sofia (Bulgaria); Popov, Todor [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, bld. Tsarigradsko chaussee 72, BG-1784 Sofia (Bulgaria)

2005-07-22

Deformed parabose and parafermi algebras are revised and endowed with Hopf structure in a natural way. The noncocommutative coproduct allows for construction of parastatistics Fock-like representations, built out of the simplest deformed Bose and Fermi representations. The construction gives rise to quadratic algebras of deformed anomalous commutation relations which define the generalized Green ansatz.

CP1 model with Hopf interaction: the quantum theory

International Nuclear Information System (INIS)

Chakraborty, B.; Ghosh, Subir; Malik, R.P.

2001-01-01

The CP 1 model with Hopf interaction is quantised following the Batalin-Tyutin (BT) prescription. In this scheme, extra BT fields are introduced which allow for the existence of only commuting first-class constraints. Explicit expression for the quantum correction to the expectation value of the energy density and angular momentum in the physical sector of this model is derived. The result shows, in the particular operator ordering prescription we have chosen to work with, that the quantum effect has the usual divergent contribution of O(ℎ 2 ) in the energy expectation value. But, interestingly the Hopf term, though topological in nature, can have a finite O(ℎ) contribution to energy density in the homotopically nontrivial topological sector. The angular momentum operator, however, is found to have no quantum correction at O(ℎ), indicating the absence of any fractional spin even at this quantum level. Finally, the extended Lagrangian incorporating the BT auxiliary fields is computed in the conventional framework of BRST formalism exploiting Faddeev-Popov technique of path integral method

Comparative analysis of sub-critical transmutation reactor concepts

International Nuclear Information System (INIS)

Chang, S. H.

1997-01-01

The long-lived nuclear wastes have been substantially generated from the light water reactor for a few decades. The toxicity of these spent fuels will be higher than that of the uranium ore, even if those will be stored in the repository more than ten thousands. Hence the means of transmuting the key long-lived nuclear wastes, primarily the minor actinides, using a hybrid proton accelerator and subcritical transmutation reactor, are proposed. Until now, the representative concepts for a subcritical transmutation reactor are the Energy Amplifier, the OMEGA project, the ATW and the MSBR. The detailed concepts and the specifications are illustrated in Table 1. The design requirements for the subcritical transmutation reactor are the high transmutation rate of long-lived nuclear wastes, safety and economics. And to propose the subcritical transmutation reactor concepts, the coolant, the target material and fuel type are carefully considered. In these aspects, the representative concepts for a subcritical transmutation reactor in Table 1 have been surveyed. The requirements for a target and a coolant are the reliable, low maintenance operation and safe operation to minimize the wastes. The reliable, low maintenance operation and safe operation to minimize the wastes. The reliable coolant must have the low melting point, high heat capacity and excellent physical properties. And the target material must have high neutron yield for a given proton condition and easy heat removal capability. Therefore in respect with the above requirements, Pb-Bi is proposed as the coolant and the target material for the subcritical reactor. Because the neutron yield for a given proton energy increases linearly with mass number up to bismuth but in heavier elements spallation events sharply increase both the neutron and heat outputs, Pb-Bi meets not only such the requirements as the above for the coolant but also those for the coolant and target, the simplification of system can be achieved

Physics analyses of an accelerator-driven sub-critical assembly

Science.gov (United States)

Naberezhnev, Dmitry G.; Gohar, Yousry; Bailey, James; Belch, Henry

2006-06-01

Physics analyses have been performed for an accelerator-driven sub-critical assembly as a part of the Argonne National Laboratory activity in preparation for a joint conceptual design with the Kharkov Institute of Physics and Technology (KIPT) of Ukraine. KIPT has a plan to construct an accelerator-driven sub-critical assembly targeted towards the medical isotope production and the support of the Ukraine nuclear industry. The external neutron source is produced either through photonuclear reactions in tungsten or uranium targets, or deuteron reactions in a beryllium target. KIPT intends using the high-enriched uranium (HEU) for the fuel of the sub-critical assembly. The main objective of this paper is to study the possibility of utilizing low-enriched uranium (LEU) fuel instead of HEU fuel without penalizing the sub-critical assembly performance, in particular the neutron flux level. In the course of this activity, several studies have been carried out to investigate the main choices for the system's parameters. The external neutron source has been characterized and a pre-conceptual target design has been developed. Several sub-critical configurations with different fuel enrichments and densities have been considered. Based on our analysis, it was shown that the performance of the LEU fuel is comparable with that of the HEU fuel. The LEU fuel sub-critical assembly with 200-MeV electron energy and 100-kW electron beam power has an average total flux of ˜2.50×10 13 n/s cm 2 in the irradiation channels. The corresponding total facility power is ˜204 kW divided into 91 and 113 kW deposited in the target and sub-critical assemblies, respectively.

Dynamic transitions in a model of the hypothalamic-pituitary-adrenal axis

Science.gov (United States)

Čupić, Željko; Marković, Vladimir M.; Maćešić, Stevan; Stanojević, Ana; Damjanović, Svetozar; Vukojević, Vladana; Kolar-Anić, Ljiljana

2016-03-01

Dynamic properties of a nonlinear five-dimensional stoichiometric model of the hypothalamic-pituitary-adrenal (HPA) axis were systematically investigated. Conditions under which qualitative transitions between dynamic states occur are determined by independently varying the rate constants of all reactions that constitute the model. Bifurcation types were further characterized using continuation algorithms and scale factor methods. Regions of bistability and transitions through supercritical Andronov-Hopf and saddle loop bifurcations were identified. Dynamic state analysis predicts that the HPA axis operates under basal (healthy) physiological conditions close to an Andronov-Hopf bifurcation. Dynamic properties of the stress-control axis have not been characterized experimentally, but modelling suggests that the proximity to a supercritical Andronov-Hopf bifurcation can give the HPA axis both, flexibility to respond to external stimuli and adjust to new conditions and stability, i.e., the capacity to return to the original dynamic state afterwards, which is essential for maintaining homeostasis. The analysis presented here reflects the properties of a low-dimensional model that succinctly describes neurochemical transformations underlying the HPA axis. However, the model accounts correctly for a number of experimentally observed properties of the stress-response axis. We therefore regard that the presented analysis is meaningful, showing how in silico investigations can be used to guide the experimentalists in understanding how the HPA axis activity changes under chronic disease and/or specific pharmacological manipulations.

Critical fluctuations in cortical models near instability

Directory of Open Access Journals (Sweden)

Matthew J. Aburn

2012-08-01

Full Text Available Computational studies often proceed from the premise that cortical dynamics operate in a linearly stable domain, where fluctuations dissipate quickly and show only short memory. Studies of human EEG, however, have shown significant autocorrelation at time lags on the scale of minutes, indicating the need to consider regimes where nonlinearities influence the dynamics. Statistical properties such as increased autocorrelation length, increased variance, power-law scaling and bistable switching have been suggested as generic indicators of the approach to bifurcation in nonlinear dynamical systems. We study temporal fluctuations in a widely-employed computational model (the Jansen-Rit model of cortical activity, examining the statistical signatures that accompany bifurcations. Approaching supercritical Hopf bifurcations through tuning of the background excitatory input, we find a dramatic increase in the autocorrelation length that depends sensitively on the direction in phase space of the input fluctuations and hence on which neuronal subpopulation is stochastically perturbed. Similar dependence on the input direction is found in the distribution of fluctuation size and duration, which show power law scaling that extends over four orders of magnitude at the Hopf bifurcation. We conjecture that the alignment in phase space between the input noise vector and the center manifold of the Hopf bifurcation is directly linked to these changes. These results are consistent with the possibility of statistical indicators of linear instability being detectable in real EEG time series. However, even in a simple cortical model, we find that these indicators may not necessarily be visible even when bifurcations are present because their expression can depend sensitively on the neuronal pathway of incoming fluctuations.

Numerical study of the effect of Navier slip on the driven cavity flow

KAUST Repository

He, Qiaolin

2009-10-01

We study the driven cavity flow using the Navier slip boundary condition. Our results have shown that the Navier slip boundary condition removes the corner singularity induced by the no-slip boundary condition. In the low Reynolds number case, the behavior of the tangential stress is examined and the results are compared with the analytic results obtained in [14]. For the high Reynolds number, we study the effect of the slip on the critical Reynolds number for Hopf bifurcation. Our results show that the first Hopf bifurcation critical Reynolds number is increasing with slip length. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Rank One Strange Attractors in Periodically Kicked Predator-Prey System with Time-Delay

Science.gov (United States)

Yang, Wenjie; Lin, Yiping; Dai, Yunxian; Zhao, Huitao

2016-06-01

This paper is devoted to the study of the problem of rank one strange attractor in a periodically kicked predator-prey system with time-delay. Our discussion is based on the theory of rank one maps formulated by Wang and Young. Firstly, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when the delayed system undergoes a Hopf bifurcation and encounters an external periodic force. Then we use the theory to the periodically kicked predator-prey system with delay, deriving the conditions for Hopf bifurcation and rank one chaos along with the results of numerical simulations.

The diffusive Lotka-Volterra predator-prey system with delay.

Science.gov (United States)

Al Noufaey, K S; Marchant, T R; Edwards, M P

2015-12-01

Semi-analytical solutions for the diffusive Lotka-Volterra predator-prey system with delay are considered in one and two-dimensional domains. The Galerkin method is applied, which approximates the spatial structure of both the predator and prey populations. This approach is used to obtain a lower-order, ordinary differential delay equation model for the system of governing delay partial differential equations. Steady-state and transient solutions and the region of parameter space, in which Hopf bifurcations occur, are all found. In some cases simple linear expressions are found as approximations, to describe steady-state solutions and the Hopf parameter regions. An asymptotic analysis for the periodic solution near the Hopf bifurcation point is performed for the one-dimensional domain. An excellent agreement is shown in comparisons between semi-analytical and numerical solutions of the governing equations. Copyright © 2015 Elsevier Inc. All rights reserved.

Dynamic Bifurcations

CERN Document Server

1991-01-01

Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems (usually ordinary differential equations), when the parameter is a slowly varying function of time. During the last decade these phenomena were observed and studied by many mathematicians, both pure and applied, from eastern and western countries, using classical and nonstandard analysis. It is the purpose of this book to give an account of these developments. The first paper, by C. Lobry, is an introduction: the reader will find here an explanation of the problems and some easy examples; this paper also explains the role of each of the other paper within the volume and their relationship to one another. CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage through Bifurcation and Limit Points. Asymptotic Theory and Applications.- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey.- V. Gautheron, E. Isambe...

A mathematical model for the control of carrier-dependent infectious diseases with direct transmission and time delay

International Nuclear Information System (INIS)

Misra, A.K.; Mishra, S.N.; Pathak, A.L.; Srivastava, P.K.; Chandra, Peeyush

2013-01-01

In this paper, a non-linear delay mathematical model for the control of carrier-dependent infectious diseases through insecticides is proposed and analyzed. In the modeling process, it is assumed that disease spreads due to direct contact between susceptibles and infectives as well as through carriers (indirect contact). Further, it is assumed that insecticides are used to kill carriers and the rate of introduction of insecticides is proportional to the density of carriers with some time lag. The model analysis suggests that as delay in using insecticides exceeds some critical value, the system loses its stability and Hopf-bifurcation occurs. The direction, stability and period of the bifurcating periodic solutions arising through Hopf-bifurcation are also analyzed using normal form concept and center manifold theory. Numerical simulation is carried out to confirm the obtained analytical results

The spatial kinetic analysis of accelerator-driven subcritical reactor

International Nuclear Information System (INIS)

Takahashi, H.; An, Y.; Chen, X.

1998-02-01

The operation of the accelerator driven reactor with subcritical condition provides a more flexible choice of the reactor materials and of design parameters. A deep subcriticality is chosen sometime from the analysis of point kinetics. When a large reactor is operated in deep subcritical condition by using a localized spallation source, the power distribution has strong spatial dependence, and point kinetics does not provide proper analysis for reactor safety. In order to analyze the spatial and energy dependent kinetic behavior in the subcritical reactor, the authors developed a computation code which is composed of two parts, the first one is for creating the group cross section and the second part solves the multi-group kinetic diffusion equations. The reactor parameters such as the cross section of fission, scattering, and energy transfer among the several energy groups and regions are calculated by using a code modified from the Monte Carlo codes MCNPA and LAHET instead of the usual analytical method of ANISN, TWOTRAN codes. Thus the complicated geometry of the accelerator driven reactor core can be precisely taken into account. The authors analyzed the subcritical minor actinide transmutor studied by Japan Atomic Energy Research Institute (JAERI) using the code

Subcriticality determination of nuclear fuel assembly by Mihalczo method

International Nuclear Information System (INIS)

Yamane, Yoshihiro; Watanabe, Shoji; Nishina, Kojiro; Miyoshi, Yoshinori; Suzaki, Takenori; Kobayashi, Iwao.

1986-01-01

To establish a technique of on-site subcriticality determination suitable for the criticality safety management of nuclear fuel assembly, the applicability of the method proposed by Mihalczo was examined with the Tank-type Critical Assembly (TCA) of the Japan Atomic Energy Research Institute. In the Mihalczo method, cross power spectral densities and auto power spectral densities are evaluated from the output currents of an ionization chamber containing 252 Cf neutron source and two neutron detectors. The principle of this method is that the spectral ratio formed by the power spectral densities mentioned can be related to the subcriticality by the help of a stochastic theory. Throughout our data processing, an improved formula taking account of the neutron extinction at a detection process was used. Up to the subcriticality of 15 dollars, the Mihalczo method agreed with the water-level worth method, which has been a standard method of reactivity determination at the TCA facility. The systems treated in the present report hold symmetry concerning the nuclear fuel configuration and the 252 Cf chamber position. It was clarified that, contrary to Mihalczo's assertion, the factor converting the spectral ratio to a subcriticality depends on subcriticality itself. (author)

Bioeconomic modelling of a prey predator system using differential ...

African Journals Online (AJOL)

Continuous type gestational delay of predators is incorporated and its effect on the dynamical behavior of the model system is analyzed. Through considering delay as a bifurcation parameter, the occurrence of Hopf bifurcation of the proposed model system with positive economic profit is shown in the neighborhood of the ...

On left Hopf algebras within the framework of inhomogeneous quantum groups for particle algebras

Energy Technology Data Exchange (ETDEWEB)

Rodriguez-Romo, Suemi [Facultad de Estudios Superiores Cuautitlan, Universidad Nacional Autonoma de Mexico (Mexico)

2012-10-15

We deal with some matters needed to construct concrete left Hopf algebras for inhomogeneous quantum groups produced as noncommutative symmetries of fermionic and bosonic creation/annihilation operators. We find a map for the bidimensional fermionic case, produced as in Manin's [Quantum Groups and Non-commutative Hopf Geometry (CRM Univ. de Montreal, 1988)] seminal work, named preantipode that fulfills all the necessary requirements to be left but not right on the generators of the algebra. Due to the complexity and importance of the full task, we consider our result as an important step that will be extended in the near future.

Continuous reactivity calculation for subcritical system

International Nuclear Information System (INIS)

Silva, Cristiano; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. da

2011-01-01

With the rise of a new generation of nuclear reactors as for existence the ADS (Accelerator-Driven System), it is important to have a fast and accurate prediction of the variation in reactivity during a possible variation in the intensity of external sources. This paper presents a formulation for the calculation of reactivity in subcritical systems using the inverse method related only to nuclear power derivatives. One of the applications of the proposed method is the possibility of developing reactimeters that allow the continuous monitoring of subcritical systems. (author)

Continuous reactivity calculation for subcritical system

Energy Technology Data Exchange (ETDEWEB)

Silva, Cristiano; Goncalves, Alessandro C.; Martinez, Aquilino S.; Silva, Fernando C. da, E-mail: cristiano@herzeleid.net, E-mail: aquilino@lmp.ufrj.br, E-mail: fernando@con.ufrj.br [Coordenacao dos Programas de Pos-Graduacao em Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear; Palma, Daniel A.P., E-mail: dapalma@cnen.gov.br [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil)

2011-07-01

With the rise of a new generation of nuclear reactors as for existence the ADS (Accelerator-Driven System), it is important to have a fast and accurate prediction of the variation in reactivity during a possible variation in the intensity of external sources. This paper presents a formulation for the calculation of reactivity in subcritical systems using the inverse method related only to nuclear power derivatives. One of the applications of the proposed method is the possibility of developing reactimeters that allow the continuous monitoring of subcritical systems. (author)

Effects of stressor characteristics on early warning signs of critical transitions and "critical coupling" in complex dynamical systems.

Science.gov (United States)

Blume, Steffen O P; Sansavini, Giovanni

2017-12-01

Complex dynamical systems face abrupt transitions into unstable and catastrophic regimes. These critical transitions are triggered by gradual modifications in stressors, which push the dynamical system towards unstable regimes. Bifurcation analysis can characterize such critical thresholds, beyond which systems become unstable. Moreover, the stochasticity of the external stressors causes small-scale fluctuations in the system response. In some systems, the decomposition of these signal fluctuations into precursor signals can reveal early warning signs prior to the critical transition. Here, we present a dynamical analysis of a power system subjected to an increasing load level and small-scale stochastic load perturbations. We show that the auto- and cross-correlations of bus voltage magnitudes increase, leading up to a Hopf bifurcation point, and further grow until the system collapses. This evidences a gradual transition into a state of "critical coupling," which is complementary to the established concept of "critical slowing down." Furthermore, we analyze the effects of the type of load perturbation and load characteristics on early warning signs and find that gradient changes in the autocorrelation provide early warning signs of the imminent critical transition under white-noise but not for auto-correlated load perturbations. Furthermore, the cross-correlation between all voltage magnitude pairs generally increases prior to and beyond the Hopf bifurcation point, indicating "critical coupling," but cannot provide early warning indications. Finally, we show that the established early warning indicators are oblivious to limit-induced bifurcations and, in the case of the power system model considered here, only react to an approaching Hopf bifurcation.

Reactor Dynamics Experiments with a Sub-Critical Assembly

International Nuclear Information System (INIS)

Miley, G.H.; Yang, Y.; Wu, L.; Momota, H.

2004-01-01

A resurgence in use of nuclear power is now underway worldwide. However due to the shutdown of many university research reactors , student laboratories must rely more heavily on use of sub-critical assemblies. Here a driven sub-critical is described that uses a cylindrical Inertial Electrostatic Confinement (IEC) device to provide a fusion neutron source. The small IEC neutron source would be inserted in a fuel element position, with its power input controlled externally at a control panel. This feature opens the way to use of the critical assembly for a number of transient experiments such as sub-critical pulsing and neutron wave propagation. That in turn adds important new insights and excitement for the student teaching laboratory

WIENER-HOPF SOLVER WITH SMOOTH PROBABILITY DISTRIBUTIONS OF ITS COMPONENTS

Directory of Open Access Journals (Sweden)

Mr. Vladimir A. Smagin

2016-12-01

Full Text Available The Wiener – Hopf solver with smooth probability distributions of its component is presented. The method is based on hyper delta approximations of initial distributions. The use of Fourier series transformation and characteristic function allows working with the random variable method concentrated in transversal axis of absc.

Mechanical weathering and rock erosion by climate-dependent subcritical cracking

Science.gov (United States)

Eppes, Martha-Cary; Keanini, Russell

2017-06-01

This work constructs a fracture mechanics framework for conceptualizing mechanical rock breakdown and consequent regolith production and erosion on the surface of Earth and other terrestrial bodies. Here our analysis of fracture mechanics literature explicitly establishes for the first time that all mechanical weathering in most rock types likely progresses by climate-dependent subcritical cracking under virtually all Earth surface and near-surface environmental conditions. We substantiate and quantify this finding through development of physically based subcritical cracking and rock erosion models founded in well-vetted fracture mechanics and mechanical weathering, theory, and observation. The models show that subcritical cracking can culminate in significant rock fracture and erosion under commonly experienced environmental stress magnitudes that are significantly lower than rock critical strength. Our calculations also indicate that climate strongly influences subcritical cracking—and thus rock weathering rates—irrespective of the source of the stress (e.g., freezing, thermal cycling, and unloading). The climate dependence of subcritical cracking rates is due to the chemophysical processes acting to break bonds at crack tips experiencing these low stresses. We find that for any stress or combination of stresses lower than a rock's critical strength, linear increases in humidity lead to exponential acceleration of subcritical cracking and associated rock erosion. Our modeling also shows that these rates are sensitive to numerous other environment, rock, and mineral properties that are currently not well characterized. We propose that confining pressure from overlying soil or rock may serve to suppress subcritical cracking in near-surface environments. These results are applicable to all weathering processes.

Reduced order models, inertial manifolds, and global bifurcations: searching instability boundaries in nuclear power systems

International Nuclear Information System (INIS)

Suarez Antola, R.

2011-01-01

is obtained. Analytical formulae are derived for the frequency of oscillation and the parameters that determine the stability of the steady states, including sub- and supercritical oincar?-Andronov- Hopf (AH) bifurcations. A Bautin's bifurcation scenario seems possible on the power-flow plane: near the boundary of stability, a region where stable steady states are surrounded by unstable limit cycles surrounded at their turn by stable limit cycles. The qualitative analytical results are compared with recent digital simulations and applications of semi-analytical bifurcation theory done with reduced order models of BWR.

Subcriticality of accelerator driven system by AESJ/JAERI working party

International Nuclear Information System (INIS)

Iwasaki, Tomohiko

2002-01-01

Under Atomic Energy Society of Japan (AESJ) and Japan Atomic Energy Research Institute (JAERI), a Working Party on Reactor Physics of Accelerator-Driven System (ADS-WP) has been set since March 1999 to review and investigate special subjects related to reactor physics research of Accelerator-Driven System (ADS). In the ADS-WP, the extensive and aggressive activity is being made by 25 professional members in the field of reactor physics in Japan. The ADS is now studying three subjects related to subcriticality of ADS; (1) calculation accuracy of subcriticality on ADS, (2) critical safety issues of ADS, and (3) theoretical review of subcriticality and its measurement methods. This paper describes two topics related to the subjects (1) and (2); one is an analysis of maximum reactivity potentially inserted to a subcritical core and the other is a benchmark proposal for checking calculation accuracy of subcriticality on ADS. The full specification of the calculation benchmark will be supplied by June 2002. Researchers from overseas, especially from Korea, are welcome to join this benchmark

Measurements relevant to simulating subcriticality in ADS facilities with blanket

International Nuclear Information System (INIS)

Titarenko, Yu. E.; Batyaev, V.F.; Borovlev, S.P.; Gladkikh, N.G.; Igumnov, M.M.; Legostaev, V.O.; Karpikhin, E.I.; Konev, V.N.; Kushnerev, Yu.T.; Popkov, V.N.; Ryazhsky, V.I.; Spiridonov, V.G.; Chernyavsky, E.V.; Shvedov, O.V.

2009-10-01

The work presents the results of determining the blanket subcriticality for a zero-power heavy water reactor MAKET at the Institute for Theoretical and Experimental Physics, Moscow. The blanket is hexagonal lattice made of 36 90%-enriched 235U fuel rods spaced 173mm apart. The subcriticality was varied from ∼0.3% to 5% by adjusting the heavy water level. The subcriticality values were calibrated using the dependence of reactivity on heavy water level. The pulsed neutron source technique was used to measure the temporal dependence of neutron field at different blanket points for the calibrated subcriticality values. The subciticality values obtained in terms of the 'inverse clock' formulae using the decay constants of the measured dependences proved to differ from the calibrated subcriticalities by not more than 7% at the average. The MCNP code-aided simulations of the experiment made has given the calibrated keff values at prescribed heavy water levels and led to the neutron field decay constants at given points, which differ on the average from their experimental values by not more than 7% too. (author)

Neutron chain length distributions in subcritical systems

International Nuclear Information System (INIS)

Nolen, S.D.; Spriggs, G.

1999-01-01

In this paper, the authors present the results of the chain-length distribution as a function of k in subcritical systems. These results were obtained from a point Monte Carlo code and a three-dimensional Monte Carlo code, MC++. Based on these results, they then attempt to explain why several of the common neutron noise techniques, such as the Rossi-α and Feynman's variance-to-mean techniques, are difficult to perform in highly subcritical systems using low-efficiency detectors

Ensuring the validity of calculated subcritical limits

International Nuclear Information System (INIS)

Clark, H.K.

1977-01-01

The care taken at the Savannah River Laboratory and Plant to ensure the validity of calculated subcritical limits is described. Close attention is given to ANSI N16.1-1975, ''Validation of Calculational Methods for Nuclear Criticality Safety.'' The computer codes used for criticality safety computations, which are listed and are briefly described, have been placed in the SRL JOSHUA system to facilitate calculation and to reduce input errors. A driver module, KOKO, simplifies and standardizes input and links the codes together in various ways. For any criticality safety evaluation, correlations of the calculational methods are made with experiment to establish bias. Occasionally subcritical experiments are performed expressly to provide benchmarks. Calculated subcritical limits contain an adequate but not excessive margin to allow for uncertainty in the bias. The final step in any criticality safety evaluation is the writing of a report describing the calculations and justifying the margin

Subcritical Water Hydrolysis of Peptides: Amino Acid Side-Chain Modifications

Science.gov (United States)

Powell, Thomas; Bowra, Steve; Cooper, Helen J.

2017-09-01

Previously we have shown that subcritical water may be used as an alternative to enzymatic digestion in the proteolysis of proteins for bottom-up proteomics. Subcritical water hydrolysis of proteins was shown to result in protein sequence coverages greater than or equal to that obtained following digestion with trypsin; however, the percentage of peptide spectral matches for the samples treated with trypsin were consistently greater than for those treated with subcritical water. This observation suggests that in addition to cleavage of the peptide bond, subcritical water treatment results in other hydrolysis products, possibly due to modifications of amino acid side chains. Here, a model peptide comprising all common amino acid residues (VQSIKCADFLHYMENPTWGR) and two further model peptides (VCFQYMDRGDR and VQSIKADFLHYENPTWGR) were treated with subcritical water with the aim of probing any induced amino acid side-chain modifications. The hydrolysis products were analyzed by direct infusion electrospray tandem mass spectrometry, either collision-induced dissociation or electron transfer dissociation, and liquid chromatography collision-induced dissociation tandem mass spectrometry. The results show preferential oxidation of cysteine to sulfinic and sulfonic acid, and oxidation of methionine. In the absence of cysteine and methionine, oxidation of tryptophan was observed. In addition, water loss from aspartic acid and C-terminal amidation were observed in harsher subcritical water conditions. [Figure not available: see fulltext.

Subcriticality determination in ADS: Valina-Booster experiments

International Nuclear Information System (INIS)

Persson, C. M.; Gudowski, W.; Fokau, A.; Bournos, V.; Fokov, Y.; Routkovskaia, C.; Serafimovich, I.; Kiyavitskaya, H.

2007-01-01

A major problem in operating a full-scale subcritical accelerator-driven system (ADS) is to ensure sufficient margin to criticality. Therefore, reliable techniques for subcriticality monitoring are required. In order to develop such techniques, a full understanding of existing reactivity determination methods is essential. In this work, reactivity determination methods, such as pulsed neutron source methods and noise methods, are studied experimentally in the subcritical facility YALINA-Booster. YALINA-Booster: The subcritical assembly YALINA-Booster: recently constructed at the Joint Institute for Power and Nuclear Research - Sosny, consists of a subcritical core driven by an external neutron source. The neutron source is a powerful neutron generator consisting of a deuteron accelerator and a target of deuterium or tritium embedded in titanium. Through (d, d) - or (d, t)-reactions neutrons are created with energy around 2.5 MeV and 14.1 MeV respectively. Neutrons are born in the centre of the core and multiply through a lead matrix fuelled with highly enriched uranium (90% and 36%). This zone is referred to as the booster zone and is surrounded by a thermal zone, moderated by polyethylene. In order to reach sufficient high effective multiplication factor, the thermal zone is fuelled by approximately one thousand rods of 10% enriched uranium dioxide in cylindrical geometry. To prevent thermal neutrons from diffusing into the fast booster zone, an interface, consisting of boron carbide and natural uranium rods, is located between the zones. YALINA-Booster has a radial graphite reflector of thickness 24 cm. Experiments: Experiments using the neutron source in pulsed mode will be presented, relying on methods such as the area method and the method of prompt neutron decay rate determination. Moreover, results from noise analysis using for instance the Feynman-α method will be presented

Subcritical tests - nuclear weapon testing under the Comprehensive Test Ban Treaty

International Nuclear Information System (INIS)

Hoeibraaten, S.

1998-10-01

The report discusses possible nuclear weapons related experiments and whether these are permitted under the 1996 Comprehensive Test Ban Treaty (CTBT). The term ''subcritical experiments'' as used in the United States includes experiments in which one studies fissile materials (so far only plutonium) under extreme conditions generated by conventional high explosives, and in which a self-sustained chain reaction never develops in the fissile material. The known facts about the American subcritical experiments are presented. There is very little reason to doubt that these experiments were indeed subcritical and therefore permitted under the CTBT. Little is known about the Russian efforts that are being made on subcritical experiments

The Hopf fibration over S8 admits no S1-subfibration

International Nuclear Information System (INIS)

Loo, B.; Verjovsky, A.

1990-10-01

It is shown that there does not exist a PL-bundle over S 8 with fibre and total space PL-manifolds homotopy equivalent to CP 3 and CP 7 respectively. Consequently, the Hopf fibration over S 8 admits no subfibration by PL-circles. (author). 27 refs

The Hopf fibration over S8 admits no S1-subfibration

International Nuclear Information System (INIS)

Loo, B.; Verjovsky, A.

1990-05-01

It is shown that there does not exist a PL-bundle over S 8 with fibre and total space PL-manifolds homotopy equivalent to CP 3 and CP 7 respectively. Consequently, the Hopf fibration over S 8 admits no subfibration by PL-circles. (author). 27 refs

Modeling of the CTEx subcritical unit using MCNPX code

International Nuclear Information System (INIS)

Santos, Avelino; Silva, Ademir X. da; Rebello, Wilson F.; Cunha, Victor L. Lassance

2011-01-01

The present work aims at simulating the subcritical unit of Army Technology Center (CTEx) namely ARGUS pile (subcritical uranium-graphite arrangement) by using the computational code MCNPX. Once such modeling is finished, it could be used in k-effective calculations for systems using natural uranium as fuel, for instance. ARGUS is a subcritical assembly which uses reactor-grade graphite as moderator of fission neutrons and metallic uranium fuel rods with aluminum cladding. The pile is driven by an Am-Be spontaneous neutron source. In order to achieve a higher value for k eff , a higher concentration of U235 can be proposed, provided it safely remains below one. (author)

Bifurcation in a buoyant horizontal laminar jet

Science.gov (United States)

Arakeri, Jaywant H.; Das, Debopam; Srinivasan, J.

2000-06-01

The trajectory of a laminar buoyant jet discharged horizontally has been studied. The experimental observations were based on the injection of pure water into a brine solution. Under certain conditions the jet has been found to undergo bifurcation. The bifurcation of the jet occurs in a limited domain of Grashof number and Reynolds number. The regions in which the bifurcation occurs has been mapped in the Reynolds number Grashof number plane. There are three regions where bifurcation does not occur. The various mechanisms that prevent bifurcation have been proposed.

Generating loop graphs via Hopf algebra in quantum field theory

International Nuclear Information System (INIS)

Mestre, Angela; Oeckl, Robert

2006-01-01

We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be evaluated directly as contributions to the connected n-point functions. The recursion proceeds by loop order and vertex number

Stochastic mixed-mode oscillations in a three-species predator-prey model

Science.gov (United States)

Sadhu, Susmita; Kuehn, Christian

2018-03-01

The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For suitable parameter values, the deterministic drift part of the model admits a folded node singularity and exhibits a singular Hopf bifurcation. We focus on the parameter regime near the Hopf bifurcation, where small amplitude oscillations exist as stable dynamics in the absence of noise. In this regime, the stochastic model admits noise-driven mixed-mode oscillations (MMOs), which capture the intermediate dynamics between two cycles of population outbreaks. We perform numerical simulations to calculate the distribution of the random number of small oscillations between successive spikes for varying noise intensities and distance to the Hopf bifurcation. We also study the effect of noise on a suitable Poincaré map. Finally, we prove that the stochastic model can be transformed into a normal form near the folded node, which can be linked to recent results on the interplay between deterministic and stochastic small amplitude oscillations. The normal form can also be used to study the parameter influence on the noise level near folded singularities.

A novel concept for CRIEC-driven subcritical research reactors

International Nuclear Information System (INIS)

Nieto, M.; Miley, G.H.

2001-01-01

A novel scheme is proposed to drive a low-power subcritical fuel assembly by means of a long Cylindrical Radially-convergent Inertial Electrostatic Confinement (CRIEC) used as a neutron source. The concept is inherently safe in the sense that the fuel assembly remains subcritical at all times. Previous work has been done for the possible implementation of CRIEC as a subcritical assembly driver for power reactors. However, it has been found that the present technology and stage of development of IEC-based neutron sources can not meet the neutron flux requirements to drive a system as big as a power reactor. Nevertheless, smaller systems, such as research and training reactors, could be successfully driven with levels of neutron flux that seem more reasonable to be achieved in the near future by IEC devices. The need for custom-made expensive nuclear fission fuel, as in the case of the TRIGA reactors, is eliminated, and the CRIEC presents substantial advantages with respect to the accelerator-driven subcritical reactors in terms of simplicity and cost. In the present paper, a conceptual design for a research/training CRIEC-driven subcritical assembly is presented, emphasizing the description, principle of operation and performance of the CRIEC neutron source, highlighting its advantages and discussing some key issues that require study for the implementation of this concept. (author)

Recent perspective on coronary artery bifurcation interventions.

Science.gov (United States)

Dash, Debabrata

2014-01-01

Coronary bifurcation lesions are frequent in routine practice, accounting for 15-20% of all lesions undergoing percutaneous coronary intervention (PCI). PCI of this subset of lesions is technically challenging and historically has been associated with lower procedural success rates and worse clinical outcomes compared with non-bifurcation lesions. The introduction of drug-eluting stents has dramatically improved the outcomes. The provisional technique of implanting one stent in the main branch remains the default approach in most bifurcation lesions. Selection of the most effective technique for an individual bifurcation is important. The use of two-stent techniques as an intention to treat is an acceptable approach in some bifurcation lesions. However, a large amount of metal is generally left unapposed in the lumen with complex two-stent techniques, which is particularly concerning for the risk of stent thrombosis. New technology and dedicated bifurcation stents may overcome some of the limitations of two-stent techniques and revolutionise the management of bifurcation PCI in the future.

Beer bottle whistling: a stochastic Hopf bifurcation

Science.gov (United States)

Boujo, Edouard; Bourquard, Claire; Xiong, Yuan; Noiray, Nicolas

2017-11-01

Blowing in a bottle to produce sound is a popular and yet intriguing entertainment. We reproduce experimentally the common observation that the bottle ``whistles'', i.e. produces a distinct tone, for large enough blowing velocity and over a finite interval of blowing angle. For a given set of parameters, the whistling frequency stays constant over time while the acoustic pressure amplitude fluctuates. Transverse oscillations of the shear layer in the bottle's neck are clearly identified with time-resolved particle image velocimetry (PIV) and proper orthogonal decomposition (POD). To account for these observations, we develop an analytical model of linear acoustic oscillator (the air in the bottle) subject to nonlinear stochastic forcing (the turbulent jet impacting the bottle's neck). We derive a stochastic differential equation and, from the associated Fokker-Planck equation and the measured acoustic pressure signals, we identify the model's parameters with an adjoint optimization technique. Results are further validated experimentally, and allow us to explain (i) the occurrence of whistling in terms of linear instability, and (ii) the amplitude of the limit cycle as a competition between linear growth rate, noise intensity, and nonlinear saturation. E. B. and N. N. acknowledge support by Repower and the ETH Zurich Foundation.

Subcritical calculation of the nuclear material warehouse

International Nuclear Information System (INIS)

Garcia M, T.; Mazon R, R.

2009-01-01

In this work the subcritical calculation of the nuclear material warehouse of the Reactor TRIGA Mark III labyrinth in the Mexico Nuclear Center is presented. During the adaptation of the nuclear warehouse (vault I), the fuel was temporarily changed to the warehouse (vault II) and it was also carried out the subcritical calculation for this temporary arrangement. The code used for the calculation of the effective multiplication factor, it was the Monte Carlo N-Particle Extended code known as MCNPX, developed by the National Laboratory of Los Alamos, for the particles transport. (Author)

International Workshop "Groups, Rings, Lie and Hopf Algebras"

CERN Document Server

2003-01-01

The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Numerical simulations of subcritical reactor kinetics in thermal hydraulic transient phases

Energy Technology Data Exchange (ETDEWEB)

Yoo, J; Park, W S [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1999-12-31

A subcritical reactor driven by a linear proton accelerator has been considered as a nuclear waste incinerator at Korea Atomic Energy Research Institute (KAERI). Since the multiplication factor of a subcritical reactor is less than unity, to compensate exponentially decreasing fission neutrons, external neutrons form spallation reactions are essentially required for operating the reactor in its steady state. Furthermore, the profile of accelerator beam currents is very important in controlling a subcritical reactor, because the reactor power varies in accordance to the profile of external neutrons. We have developed a code system to find numerical solutions of reactor kinetics equations, which are the simplest dynamic model for controlling reactors. In a due course of our previous numerical study of point kinetics equations for critical reactors, however, we learned that the same code system can be used in studying dynamic behavior of the subcritical reactor. Our major motivation of this paper is to investigate responses of subcritical reactors for small changes in thermal hydraulic parameters. Building a thermal hydraulic model for the subcritical reactor dynamics, we performed numerical simulations for dynamic responses of the reactor based on point kinetics equations with a source term. Linearizing a set of coupled differential equations for reactor responses, we focus our research interest on dynamic responses of the reactor to variations of the thermal hydraulic parameters in transient phases. 5 refs., 8 figs. (Author)

Numerical simulations of subcritical reactor kinetics in thermal hydraulic transient phases

Energy Technology Data Exchange (ETDEWEB)

Yoo, J.; Park, W. S. [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

1998-12-31

A subcritical reactor driven by a linear proton accelerator has been considered as a nuclear waste incinerator at Korea Atomic Energy Research Institute (KAERI). Since the multiplication factor of a subcritical reactor is less than unity, to compensate exponentially decreasing fission neutrons, external neutrons form spallation reactions are essentially required for operating the reactor in its steady state. Furthermore, the profile of accelerator beam currents is very important in controlling a subcritical reactor, because the reactor power varies in accordance to the profile of external neutrons. We have developed a code system to find numerical solutions of reactor kinetics equations, which are the simplest dynamic model for controlling reactors. In a due course of our previous numerical study of point kinetics equations for critical reactors, however, we learned that the same code system can be used in studying dynamic behavior of the subcritical reactor. Our major motivation of this paper is to investigate responses of subcritical reactors for small changes in thermal hydraulic parameters. Building a thermal hydraulic model for the subcritical reactor dynamics, we performed numerical simulations for dynamic responses of the reactor based on point kinetics equations with a source term. Linearizing a set of coupled differential equations for reactor responses, we focus our research interest on dynamic responses of the reactor to variations of the thermal hydraulic parameters in transient phases. 5 refs., 8 figs. (Author)

Reaction kinetics of cellulose hydrolysis in subcritical and supercritical water

Science.gov (United States)

Olanrewaju, Kazeem Bode

The uncertainties in the continuous supply of fossil fuels from the crisis-ridden oil-rich region of the world is fast shifting focus on the need to utilize cellulosic biomass and develop more efficient technologies for its conversion to fuels and chemicals. One such technology is the rapid degradation of cellulose in supercritical water without the need for an enzyme or inorganic catalyst such as acid. This project focused on the study of reaction kinetics of cellulose hydrolysis in subcritical and supercritical water. Cellulose reactions at hydrothermal conditions can proceed via the homogeneous route involving dissolution and hydrolysis or the heterogeneous path of surface hydrolysis. The work is divided into three main parts. First, the detailed kinetic analysis of cellulose reactions in micro- and tubular reactors was conducted. Reaction kinetics models were applied, and kinetics parameters at both subcritical and supercritical conditions were evaluated. The second major task was the evaluation of yields of water soluble hydrolysates obtained from the hydrolysis of cellulose and starch in hydrothermal reactors. Lastly, changes in molecular weight distribution due to hydrothermolytic degradation of cellulose were investigated. These changes were also simulated based on different modes of scission, and the pattern generated from simulation was compared with the distribution pattern from experiments. For a better understanding of the reaction kinetics of cellulose in subcritical and supercritical water, a series of reactions was conducted in the microreactor. Hydrolysis of cellulose was performed at subcritical temperatures ranging from 270 to 340 °C (tau = 0.40--0.88 s). For the dissolution of cellulose, the reaction was conducted at supercritical temperatures ranging from 375 to 395 °C (tau = 0.27--0.44 s). The operating pressure for the reactions at both subcritical and supercritical conditions was 5000 psig. The results show that the rate-limiting step in

Study on uranium-water multiplicative means of the (RESUCO-Subcritical experimental reactor of uranium with oxygen) subcritical assembly by pulsed neutron technique

International Nuclear Information System (INIS)

Jesus Barbosa, S. de.

1987-01-01

The effective multiplication factor and the nuclear parameters associated with the variation of (RESUCO- Subcritical Experimental Reactor of Uranium with Oxygen) Subcritical Assembly Configuration, using pulsed neutron technique are analysed. BF3 detectors were used to detect the variation of thermal neutrons in the system, positioned parallelly to fuel elements, and a proton recoil detector was used for monitoring the neutron generation. (M.C.K.) [pt

A modified Leslie-Gower predator-prey interaction model and parameter identifiability

Science.gov (United States)

Tripathi, Jai Prakash; Meghwani, Suraj S.; Thakur, Manoj; Abbas, Syed

2018-01-01

In this work, bifurcation and a systematic approach for estimation of identifiable parameters of a modified Leslie-Gower predator-prey system with Crowley-Martin functional response and prey refuge is discussed. Global asymptotic stability is discussed by applying fluctuation lemma. The system undergoes into Hopf bifurcation with respect to parameters intrinsic growth rate of predators (s) and prey reserve (m). The stability of Hopf bifurcation is also discussed by calculating Lyapunov number. The sensitivity analysis of the considered model system with respect to all variables is performed which also supports our theoretical study. To estimate the unknown parameter from the data, an optimization procedure (pseudo-random search algorithm) is adopted. System responses and phase plots for estimated parameters are also compared with true noise free data. It is found that the system dynamics with true set of parametric values is similar to the estimated parametric values. Numerical simulations are presented to substantiate the analytical findings.

Systematic parameter study of dynamo bifurcations in geodynamo simulations

Science.gov (United States)

Petitdemange, Ludovic

2018-04-01

We investigate the nature of the dynamo bifurcation in a configuration applicable to the Earth's liquid outer core, i.e. in a rotating spherical shell with thermally driven motions with no-slip boundaries. Unlike in previous studies on dynamo bifurcations, the control parameters have been varied significantly in order to deduce general tendencies. Numerical studies on the stability domain of dipolar magnetic fields found a dichotomy between non-reversing dipole-dominated dynamos and the reversing non-dipole-dominated multipolar solutions. We show that, by considering weak initial fields, the above transition disappears and is replaced by a region of bistability for which dipolar and multipolar dynamos coexist. Such a result was also observed in models with free-slip boundaries in which the geostrophic zonal flow can develop and participate to the dynamo mechanism for non-dipolar fields. We show that a similar process develops in no-slip models when viscous effects are reduced sufficiently. The following three regimes are distinguished: (i) Close to the onset of convection (Rac) with only the most critical convective mode (wave number) being present, dynamos set in supercritically in the Ekman number regime explored here and are dipole-dominated. Larger critical magnetic Reynolds numbers indicate that they are particularly inefficient. (ii) in the range 3 10) , the relative importance of zonal flows increases with Ra in non-magnetic models. The field topology depends on the magnitude of the initial magnetic field. The dipolar branch has a subcritical behavior whereas the multipolar branch has a supercritical behavior. By approaching more realistic parameters, the extension of this bistable regime increases. A hysteretic behavior questions the common interpretation for geomagnetic reversals. Far above the dynamo threshold (by increasing the magnetic Prandtl number), Lorentz forces contribute to the first order force balance, as predicted for planetary dynamos. When

Subcritical reactivity measurement at Angra 1 nuclear power plant

International Nuclear Information System (INIS)

Kuramoto, Renato Yoichi Ribeiro; Miranda, Anselmo Ferreira

2011-01-01

In order to speed up the Angra 1 NPP physics tests, this work intends to develop a digital reactivity meter combined with a methodology of the modified Neutron Source Multiplication (NSM) method with correction factors for subcriticality measurements at Angra 1 NPP. In the first part of this work, we have applied the Modified Neutron Source Multiplication (MNSM) Method with fundamental mode extraction, in order to improve the monitoring of the subcriticality at Angra 1 NPP during the criticality approach. In the second part, we developed a preliminary subcritical reactivity meter algorithm based on the point-reactor inverse kinetic model with six delayed neutron groups and external neutron source. The source strength was obtained through the Least Squares Inverse Kinetics Method (LSIKM). (author)

Physics of subcritical multiplying regions and experimental validation

International Nuclear Information System (INIS)

Salvatores, M.

1996-01-01

The coupling of a particle accelerator with a spallation target and with a subcritical multiplying region has been proposed in the fifties and is called here a hybrid system. This article gives some ideas about the energetic balance of such a system. The possibilities of experimental validation of some properties of a subcritical multiplying region by using MASURCA facility at CEA-Cadarache are examined. The results of a preliminary experiment called MUSE are presented. (A.C.)

Pulsed neutron source based on accelerator-subcritical-assembly

Energy Technology Data Exchange (ETDEWEB)

Inoue, Makoto; Noda, Akira; Iwashita, Yoshihisa; Okamoto, Hiromi; Shirai, Toshiyuki [Kyoto Univ., Uji (Japan). Inst. for Chemical Research

1997-03-01

A new pulsed neutron source which consists of a 300MeV proton linac and a nuclear fuel subcritical assembly is proposed. The proton linac produces pulsed spallation neutrons, which are multipied by the subcritical assembly. A prototype proton linac that accelerates protons up to 7MeV has been developed and a high energy section of a DAW structure is studied with a power model. Halo formations in high intensity beam are also being studied. (author)

Part 2: Dynamics of magnetic oscillator

International Nuclear Information System (INIS)

Anon.

1987-01-01

This is an experimental study of a forced symmetric oscillator containing a saturable inductor with magnetic hysteresis. It displays a Hopf bifurcation to quasiperiodicity, entrainment horns, and chaos. The bifurcations and hysteresis occurring near points of resonance (particularly ''strong resonance'') are studied in detail and it is shown how the observed behavior can be understood using Arnold's theory. Much of the behavior relating to the entrainment horns is explored: period doubling and symmetry breaking bifurcations; homoclinic bifurcations; and crises and other bifurcations taking place at the horn boundaries. Important features of the behavior related to symmetry properties of the oscillator are studied and explained through the concept of a half-cycle map. The system is shown to exhibit a Hopf bifurcation from a phase-locked state to periodic ''islands,'' similar to those found in Hamiltonian systems. An initialization technique is used to observe the manifolds of saddle orbits and other hidden structure. An unusual differential equation model is developed which is irreversible and generates a noninvertible Poincare map of the plane. Noninvertibility of this planar map has important effects on the behavior observed. The Poincare map may also be approximated through experimental measurements, resulting in a planar map with parameter dependence. This model gives good correspondence with the system in a region of the parameter space. 31 refs., 36 figs., 1 tab

Macular variant of acrokeratosis verruciformis of Hopf

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Rita Vipul Vora

2017-01-01

Full Text Available Acrokeratosis verruciformis (AKV of Hopf is an autosomal dominant condition characterized by multiple flesh-colored or lightly pigmented flat or convex warty papules over dorsa of hands, feet, knees, elbows, and forearms. It affects both sexes and is usually present at birth or appears in early childhood. Two forms of the disease have been described, namely, classical AKV and sporadic AKV. Histological examination differentiates it from other similar conditions. Superficial ablation is the treatment of choice. We represent a case of a young female with extensive lesions over contralateral limbs, of classical AKV interspersed with multiple hypopigmented macular lesions of AKV.

Voltage stability, bifurcation parameters and continuation methods

Energy Technology Data Exchange (ETDEWEB)

Alvarado, F L [Wisconsin Univ., Madison, WI (United States)

1994-12-31

This paper considers the importance of the choice of bifurcation parameter in the determination of the voltage stability limit and the maximum power load ability of a system. When the bifurcation parameter is power demand, the two limits are equivalent. However, when other types of load models and bifurcation parameters are considered, the two concepts differ. The continuation method is considered as a method for determination of voltage stability margins. Three variants of the continuation method are described: the continuation parameter is the bifurcation parameter the continuation parameter is initially the bifurcation parameter, but is free to change, and the continuation parameter is a new `arc length` parameter. Implementations of voltage stability software using continuation methods are described. (author) 23 refs., 9 figs.

Dynamic analysis of multiple nuclear-coupled boiling channels based on a multi-point reactor model

International Nuclear Information System (INIS)

Lee, J.D.; Pan Chin

2005-01-01

This work investigates the non-linear dynamics and stabilities of a multiple nuclear-coupled boiling channel system based on a multi-point reactor model using the Galerkin nodal approximation method. The nodal approximation method for the multiple boiling channels developed by Lee and Pan [Lee, J.D., Pan, C., 1999. Dynamics of multiple parallel boiling channel systems with forced flows. Nucl. Eng. Des. 192, 31-44] is extended to address the two-phase flow dynamics in the present study. The multi-point reactor model, modified from Uehiro et al. [Uehiro, M., Rao, Y.F., Fukuda, K., 1996. Linear stability analysis on instabilities of in-phase and out-of-phase modes in boiling water reactors. J. Nucl. Sci. Technol. 33, 628-635], is employed to study a multiple-channel system with unequal steady-state neutron density distribution. Stability maps, non-linear dynamics and effects of major parameters on the multiple nuclear-coupled boiling channel system subject to a constant total flow rate are examined. This study finds that the void-reactivity feedback and neutron interactions among subcores are coupled and their competing effects may influence the system stability under different operating conditions. For those cases with strong neutron interaction conditions, by strengthening the void-reactivity feedback, the nuclear-coupled effect on the non-linear dynamics may induce two unstable oscillation modes, the supercritical Hopf bifurcation and the subcritical Hopf bifurcation. Moreover, for those cases with weak neutron interactions, by quadrupling the void-reactivity feedback coefficient, period-doubling and complex chaotic oscillations may appear in a three-channel system under some specific operating conditions. A unique type of complex chaotic attractor may evolve from the Rossler attractor because of the coupled channel-to-channel thermal-hydraulic and subcore-to-subcore neutron interactions. Such a complex chaotic attractor has the imbedding dimension of 5 and the

Activity report of working party on reactor physics of subcritical system. October 2001 to March 2003

International Nuclear Information System (INIS)

2004-03-01

Under the Research Committee on Reactor Physics, the Working Party on Reactor Physics of Subcritical System (ADS-WP) was set in July 2001 to research reactor physics of subcritical system such as Accelerator-Driven System (ADS). The WP, at the first meeting, discussed a guideline of its activity for two years and decided to perform theoretical research for the following subjects: (1) study of reactor physics for a subcritical core, (2) benchmark problems for a subcritical core and their calculations, (3) study of physical parameters affecting to set subcriticality of ADS, and (4) study of measurement and surveillance methods of subcriticality of a subcritical core. The activity of ADS-WP continued up to March 2003. In this duration, the members of the WP met together eight times, including four meetings jointly held with the Workshop on Accelerator-Driven Subcritical Reactor at Kyoto University Research Reactor Institute. This report summarizes the result obtained by the above WP activity and research. (author)

The genesis of period-adding bursting without bursting-chaos in the Chay model

International Nuclear Information System (INIS)

Yang Zhuoqin; Lu Qishao; Li Li

2006-01-01

According to the period-adding firing patterns without chaos observed in neuronal experiments, the genesis of the period-adding 'fold/homoclinic' bursting sequence without bursting-chaos is explored by numerical simulation, fast/slow dynamics and bifurcation analysis of limit cycle in the neuronal Chay model. It is found that each periodic bursting, from period-1 to 7, is separately generated by the corresponding periodic spiking pattern through two period-doubling bifurcations, except for the period-1 bursting occurring via a Hopf bifurcation. Consequently, it can be revealed that this period-adding bursting bifurcation without chaos has a compound bifurcation structure with transitions from spiking to bursting, which is closely related to period-doubling bifurcations of periodic spiking in essence

Some neutronics of innovative subcritical assembly with fast neutron spectrum

International Nuclear Information System (INIS)

Kiyavitskaya, H.; Fokov, Yu.; Rutkovskaya, Ch.; Sadovich, S.; Kasuk, D.; Gohar, Y.; Bolshinsky, I.

2013-01-01

Conclusion: • New assembly can be used to: • develop the experimental techniques and adapt the existing ones for monitoring the sub-criticality level, neutron spectra measurements, etc; • study the spatial kinetics of sub-critical and critical systems with fast neutron spectra; • measure the transmutation reaction rates of minor-actinides etc

Rota-Baxter algebras and the Hopf algebra of renormalization

Energy Technology Data Exchange (ETDEWEB)

Ebrahimi-Fard, K.

2006-06-15

Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

Rota-Baxter algebras and the Hopf algebra of renormalization

International Nuclear Information System (INIS)

Ebrahimi-Fard, K.

2006-06-01

Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

Bifurcation of solutions to Hamiltonian boundary value problems

Science.gov (United States)

McLachlan, R. I.; Offen, C.

2018-06-01

A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of equilibria, bifurcations of boundary value problems are global in nature and may not be related to any obvious change in dynamical behaviour. Catastrophe theory is a well-developed framework which studies the bifurcations of critical points of functions. In this paper we study the bifurcations of solutions of boundary-value problems for symplectic maps, using the language of (finite-dimensional) singularity theory. We associate certain such problems with a geometric picture involving the intersection of Lagrangian submanifolds, and hence with the critical points of a suitable generating function. Within this framework, we then study the effect of three special cases: (i) some common boundary conditions, such as Dirichlet boundary conditions for second-order systems, restrict the possible types of bifurcations (for example, in generic planar systems only the A-series beginning with folds and cusps can occur); (ii) integrable systems, such as planar Hamiltonian systems, can exhibit a novel periodic pitchfork bifurcation; and (iii) systems with Hamiltonian symmetries or reversing symmetries can exhibit restricted bifurcations associated with the symmetry. This approach offers an alternative to the analysis of critical points in function spaces, typically used in the study of bifurcation of variational problems, and opens the way to the detection of more exotic bifurcations than the simple folds and cusps that are often found in examples.

Energetics and monsoon bifurcations

Science.gov (United States)

Seshadri, Ashwin K.

2017-01-01

Monsoons involve increases in dry static energy (DSE), with primary contributions from increased shortwave radiation and condensation of water vapor, compensated by DSE export via horizontal fluxes in monsoonal circulations. We introduce a simple box-model characterizing evolution of the DSE budget to study nonlinear dynamics of steady-state monsoons. Horizontal fluxes of DSE are stabilizing during monsoons, exporting DSE and hence weakening the monsoonal circulation. By contrast latent heat addition (LHA) due to condensation of water vapor destabilizes, by increasing the DSE budget. These two factors, horizontal DSE fluxes and LHA, are most strongly dependent on the contrast in tropospheric mean temperature between land and ocean. For the steady-state DSE in the box-model to be stable, the DSE flux should depend more strongly on the temperature contrast than LHA; stronger circulation then reduces DSE and thereby restores equilibrium. We present conditions for this to occur. The main focus of the paper is describing conditions for bifurcation behavior of simple models. Previous authors presented a minimal model of abrupt monsoon transitions and argued that such behavior can be related to a positive feedback called the `moisture advection feedback'. However, by accounting for the effect of vertical lapse rate of temperature on the DSE flux, we show that bifurcations are not a generic property of such models despite these fluxes being nonlinear in the temperature contrast. We explain the origin of this behavior and describe conditions for a bifurcation to occur. This is illustrated for the case of the July-mean monsoon over India. The default model with mean parameter estimates does not contain a bifurcation, but the model admits bifurcation as parameters are varied.

Bifurcations of non-smooth systems

Science.gov (United States)

Angulo, Fabiola; Olivar, Gerard; Osorio, Gustavo A.; Escobar, Carlos M.; Ferreira, Jocirei D.; Redondo, Johan M.

2012-12-01

Non-smooth systems (namely piecewise-smooth systems) have received much attention in the last decade. Many contributions in this area show that theory and applications (to electronic circuits, mechanical systems, …) are relevant to problems in science and engineering. Specially, new bifurcations have been reported in the literature, and this was the topic of this minisymposium. Thus both bifurcation theory and its applications were included. Several contributions from different fields show that non-smooth bifurcations are a hot topic in research. Thus in this paper the reader can find contributions from electronics, energy markets and population dynamics. Also, a carefully-written specific algebraic software tool is presented.

Extraction of antioxidants from Chlorella sp. using subcritical water treatment

Science.gov (United States)

Zakaria, S. M.; Mustapa Kamal, S. M.; Harun, M. R.; Omar, R.; Siajam, S. I.

2017-06-01

Chlorella sp. microalgae is one of the main source of natural bioactive compounds used in the food and pharmaceutical industries. Subcritical water extraction is the technique that offers an efficient, non-toxic, and environmental-friendly method to obtain natural ingredients. In this work, the extracts of Chlorella sp. microalgae was evaluated in terms of: chemical composition, extraction (polysaccharides) yield and antioxidant activity, using subcritical water extraction. Extractions were performed at temperatures ranging from 100°C to 300°C. The results show that by using subcritical water, the highest yield of polysaccharides is 23.6 that obtained at 150°C. Analysis on the polysaccharides yield show that the contents were highly influenced by the extraction temperature. The individual antioxidant activity were evaluated by in vitro assay using a free radical method. In general, the antioxidant activity of the extracts obtained at different water temperatures was high, with values of 31.08-54.29 . The results indicated that extraction by subcritical water was effective and Chlorella sp. can be a useful source of natural antioxidants.

Second Hopf map and supersymmetric mechanics with Yang monopole

International Nuclear Information System (INIS)

Gonzales, M.; Toppan, F.; Kuznetsova, Z.; Nersessian, F.; Yeghikyan, V.

2009-01-01

We propose to use the second Hopf map for the reduction (via SU(2) group action) of the eight-dimensional supersymmetric mechanics to five-dimensional supersymmetric systems specified by the presence of an SU(2) Yang monopole. For our purpose we develop the relevant Lagrangian reduction procedure. The reduced system is characterized by its invariance under the N = 5 or N = 4 supersymmetry generators (with or without an additional conserved BRST charge operator) which commute with the su(2) generators. (author)

Physics study of D-D/D-T neutron driven experimental subcritical assembly

International Nuclear Information System (INIS)

Sinha, Amar

2015-01-01

An experimental program to design and study external source driven subcritical assembly has been initiated at BARC. This program is aimed at understanding neutronic characteristics of accelerator driven system at low power level. In this series, a zero-power, sub-critical assembly driven by a D-D/D-T neutron generator has been developed. This system is modular in design and it is first in the series of subcritical assemblies being designed. The subcritical core consists of natural uranium fuel with high density polyethylene as moderator and beryllium oxide as reflector. The subcritical core is coupled to Purnima Neutron Generator. Preliminary experiments have been carried out for spatial flux measurement and reactivity estimation using pulsed neutron source (PNS) techniques. Further experiments are being planned to measure the reactivity and other kinetic parameters using noise methods. This facility would also be used for carrying out studies on effect of source importance and measurement of source multiplication factor k s and external neutron source efficiency φ* in great details. Some experiments with D-D and D-T neutrons have been presented. (author)

Modeling of Parameters of Subcritical Assembly SAD

CERN Document Server

Petrochenkov, S; Puzynin, I

2005-01-01

The accepted conceptual design of the experimental Subcritical Assembly in Dubna (SAD) is based on the MOX core with a nominal unit capacity of 25 kW (thermal). This corresponds to the multiplication coefficient $k_{\\rm eff} =0.95$ and accelerator beam power 1 kW. A subcritical assembly driven with the existing 660 MeV proton accelerator at the Joint Institute for Nuclear Research has been modelled in order to make choice of the optimal parameters for the future experiments. The Monte Carlo method was used to simulate neutron spectra, energy deposition and doses calculations. Some of the calculation results are presented in the paper.

Evaluating Subcriticality during the Ebola Epidemic in West Africa.

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Wayne T A Enanoria

Full Text Available The 2014-2015 Ebola outbreak is the largest and most widespread to date. In order to estimate ongoing transmission in the affected countries, we estimated the weekly average number of secondary cases caused by one individual infected with Ebola throughout the infectious period for each affected West African country using a stochastic hidden Markov model fitted to case data from the World Health Organization. If the average number of infections caused by one Ebola infection is less than 1.0, the epidemic is subcritical and cannot sustain itself. The epidemics in Liberia and Sierra Leone have approached subcriticality at some point during the epidemic; the epidemic in Guinea is ongoing with no evidence that it is subcritical. Response efforts to control the epidemic should continue in order to eliminate Ebola cases in West Africa.

Methods for the reactivity evaluation in subcritical systems analysis: a review

International Nuclear Information System (INIS)

Dulla, S.; Picca, P.; Carta, M.

2011-01-01

The assessment of the subcritical source-driven system technology for waste incineration and power production requires the development of reliable and efficient techniques for the reactivity evaluation and monitoring. Starting from the standard methods developed for close-to-criticality systems, extensive research activities have been carried out to analyze the behavior of subcritical assembly in time-dependent condition and to infer the subcriticality level from local flux values. In the present work, a review of some key aspects in the method development for ADS analysis is proposed, with special attention to the techniques for reactivity evaluation. (author)

Analysis of neutronics and dynamic characteristics with reactivity injection in LBE cooled sub-critical reactor

International Nuclear Information System (INIS)

Chen Sen; Wu Yican; Jin Ming; Chen Zhibin; Bai Yunqing; Zhao Zhumin

2014-01-01

Accelerator Driven Sub-critical System (ADS) has particular neutronics behaviors compared with the critical system. Prompt jump approximation point reactor kinetics equations taken external source into account have been deduced using an approach of prompt jump approximation. And the relationship between injection reactivity and power ampliation has been achieved. In addition, based on the RELAP5 code the prolong development of point reactor kinetics code used into assessing sub-critical system have been promoted. Different sub-criticality (k eff = 0.90, 0.95, 0.97, 0.98 and 0.99) have been assessed in preliminary design of a type of natural circulation cooling sub-critical reactor under conditions of reactivity injection +1 β in one second. It shows that the external source prompt transient approximation method has an accurate solution after injecting reactivity around short time and has a capacity to solve the dynamic equation, and the sub-critical system has an inner stability while the deeper sub-criticality the less impact on the sub-critical system. (authors)

Analysis of Vehicle Steering and Driving Bifurcation Characteristics

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Xianbin Wang

2015-01-01

Full Text Available The typical method of vehicle steering bifurcation analysis is based on the nonlinear autonomous vehicle model deriving from the classic two degrees of freedom (2DOF linear vehicle model. This method usually neglects the driving effect on steering bifurcation characteristics. However, in the steering and driving combined conditions, the tyre under different driving conditions can provide different lateral force. The steering bifurcation mechanism without the driving effect is not able to fully reveal the vehicle steering and driving bifurcation characteristics. Aiming at the aforementioned problem, this paper analyzed the vehicle steering and driving bifurcation characteristics with the consideration of driving effect. Based on the 5DOF vehicle system dynamics model with the consideration of driving effect, the 7DOF autonomous system model was established. The vehicle steering and driving bifurcation dynamic characteristics were analyzed with different driving mode and driving torque. Taking the front-wheel-drive system as an example, the dynamic evolution process of steering and driving bifurcation was analyzed by phase space, system state variables, power spectral density, and Lyapunov index. The numerical recognition results of chaos were also provided. The research results show that the driving mode and driving torque have the obvious effect on steering and driving bifurcation characteristics.

Dynamics in a Delayed Neural Network Model of Two Neurons with Inertial Coupling

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Changjin Xu

2012-01-01

Full Text Available A delayed neural network model of two neurons with inertial coupling is dealt with in this paper. The stability is investigated and Hopf bifurcation is demonstrated. Applying the normal form theory and the center manifold argument, we derive the explicit formulas for determining the properties of the bifurcating periodic solutions. An illustrative example is given to demonstrate the effectiveness of the obtained results.

Signal Processing, Pattern Formation and Adaptation in Neural Oscillators

Science.gov (United States)

2016-11-29

rhythmic patterns. As such, our models are appropriate for describing various phenomena in the auditory system, including critical nonlinear...several distinct intrinsic behaviors available near a Hopf bifurcation or a Bautin (a.k.a. double limit cycle) bifurcation. Stability analysis shows...example the perception of pitch at event timescales (Meddis & O’Mard, 2006) and the perception of pulse and meter at rhythmic timescales (Large

Indeterminacy and stability in a modified Romer model

Czech Academy of Sciences Publication Activity Database

Slobodyan, Sergey

2007-01-01

Roč. 29, č. 1 (2007), s. 169-177 ISSN 0164-0704 Institutional research plan: CEZ:MSM0021620846 Keywords : indeterminacy * Hopf bifurcation * Romer model Subject RIV: AH - Economics Impact factor: 0.360, year: 2007

Attractors near grazing–sliding bifurcations

International Nuclear Information System (INIS)

Glendinning, P; Kowalczyk, P; Nordmark, A B

2012-01-01

In this paper we prove, for the first time, that multistability can occur in three-dimensional Fillipov type flows due to grazing–sliding bifurcations. We do this by reducing the study of the dynamics of Filippov type flows around a grazing–sliding bifurcation to the study of appropriately defined one-dimensional maps. In particular, we prove the presence of three qualitatively different types of multiple attractors born in grazing–sliding bifurcations. Namely, a period-two orbit with a sliding segment may coexist with a chaotic attractor, two stable, period-two and period-three orbits with a segment of sliding each may coexist, or a non-sliding and period-three orbit with two sliding segments may coexist

Choosing the optimal parameters of subcritical reactors driven by accelerators

International Nuclear Information System (INIS)

Khudaverdyan, A.G.; Zhamkochyan, V.M.

1998-03-01

Physical aspects of a subcritical Nuclear Power Plants (NPP) driven by proton accelerators are considered. Estimated theoretical calculations are made for subcritical regimes of various types of reactors. It was shown that the creation of the quite effective explosion-safe NPP is real at an existing level of the accelerator technique by using available reactor units (including the serial ones). (author)

Bifurcation with memory

International Nuclear Information System (INIS)

Olmstead, W.E.; Davis, S.H.; Rosenblat, S.; Kath, W.L.

1986-01-01

A model equation containing a memory integral is posed. The extent of the memory, the relaxation time lambda, controls the bifurcation behavior as the control parameter R is increased. Small (large) lambda gives steady (periodic) bifurcation. There is a double eigenvalue at lambda = lambda 1 , separating purely steady (lambda 1 ) from combined steady/T-periodic (lambda > lambda 1 ) states with T → infinity as lambda → lambda + 1 . Analysis leads to the co-existence of stable steady/periodic states and as R is increased, the periodic states give way to the steady states. Numerical solutions show that this behavior persists away from lambda = lambda 1

A case study in bifurcation theory

Science.gov (United States)

Khmou, Youssef

This short paper is focused on the bifurcation theory found in map functions called evolution functions that are used in dynamical systems. The most well-known example of discrete iterative function is the logistic map that puts into evidence bifurcation and chaotic behavior of the topology of the logistic function. We propose a new iterative function based on Lorentizan function and its generalized versions, based on numerical study, it is found that the bifurcation of the Lorentzian function is of second-order where it is characterized by the absence of chaotic region.

Twisting products in Hopf algebras and the construction of the quantum double

International Nuclear Information System (INIS)

Ferrer Santos, W.R.

1992-04-01

Let H be a finite dimensional Hopf algebra and B an (H, H*)-comodule algebra. The purpose of this note is to present a construction in which the product of B is twisted by the given actions. The constructions of the smash product and of the Quantum Double appear as special cases. (author). 7 refs

Transient subcritical crack-growth behavior in transformation-toughened ceramics

International Nuclear Information System (INIS)

Dauskardt, R.H.; Ritchie, R.O.; Carter, W.C.; Veirs, D.K.

1990-01-01

Transient subcritical crack-growth behavior following abrupt changes in the applied load are studied in transformation-toughened ceramics. A mechanics analysis is developed to model the transient nature of transformation shielding of the crack tip, K s , with subcritical crack extension following the applied load change. conditions for continued crack growth, crack growth followed by arrest, and no crack growth after the load change, are considered and related to the magnitude and sign of the applied load change and to materials properties such as the critical transformation stress. The analysis is found to provide similar trends in K s compared to values calculated from experimentally measured transformation zones in a transformation-toughened Mg-PSZ. In addition, accurate prediction of the post load-change transient crack-growth behavior is obtained using experimentally derived steady-state subcritical crack-growth relationships for cyclic fatigue in the same material

Research Article

African Journals Online (AJOL)

2018-01-01

Jan 1, 2018 ... factory of hydrocarbon treatment. .... this energy of the fluid transforms into a rotating mechanical energy on a shaft allowing a .... Hopf bifurcations in gas turbine combustors, International Journal of Non-Linear Mechanics,.

The genesis of period-adding bursting without bursting-chaos in the Chay model

International Nuclear Information System (INIS)

Yang Zhuoqin; Lu Qishao; Li Li

2006-01-01

According to the period-adding firing patterns without chaos observed in neuronal experiments, the genesis of the period-adding 'fold/homoclinic' bursting sequence without bursting-chaos is explored by numerical simulation, fast/slow dynamics and bifurcation analysis of limit cycle in the neuronal Chay model. It is found that each periodic bursting, from period-1 to period-7, is separately generated by the corresponding periodic spiking pattern through two period-doubling bifurcations, except for the period-1 bursting occurring via a Hopf bifurcation. Consequently, it can be revealed that this period-adding bursting bifurcation without chaos has a compound bifurcation structure with transitions from spiking to bursting, which is closely related to period-doubling bifurcations of periodic spiking in essence

Amplitude equations for a sub-diffusive reaction-diffusion system

International Nuclear Information System (INIS)

Nec, Y; Nepomnyashchy, A A

2008-01-01

A sub-diffusive reaction-diffusion system with a positive definite memory operator and a nonlinear reaction term is analysed. Amplitude equations (Ginzburg-Landau type) are derived for short wave (Turing) and long wave (Hopf) bifurcation points

Indeterminacy and stability in a modified Romer model: a general case

Czech Academy of Sciences Publication Activity Database

Slobodyan, Sergey

-, č. 284 (2006), s. 1-16 ISSN 1211-3298 Institutional research plan: CEZ:AV0Z70850503 Keywords : indeterminacy * stability * Hopf bifurcation Subject RIV: AH - Economics http://www.cerge-ei.cz/pdf/wp/Wp284.pdf

Quantum entanglement and fixed-point bifurcations

International Nuclear Information System (INIS)

Hines, Andrew P.; McKenzie, Ross H.; Milburn, G.J.

2005-01-01

How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state--the ground state--achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation

Solubility of Benzo[a]pyrene and Organic Matter of Soil in Subcritical Water

Directory of Open Access Journals (Sweden)

Svetlana Sushkova

2015-12-01

Full Text Available A dynamic subcritical water extraction method of benzo[a]pyrene from soils is under consideration. The optimum conditions for benzo[a]pyrene extraction from soil are described including the soil treatment by subcritical water at 250 °C and 100 atm for 30 min. The effectiveness of developed method was determined using the matrix spiking recovery technique. A comparative analysis was made to evaluate the results of benzo[a]pyrene extraction from soils using the subcritical water and organic solvents. The advantages of the subcritical water extraction involve the use of ecologically friendly solvent, a shorter time for the analysis and a higher amount of benzo[a]pyrene extracted from soil (96 %. The influence of subcritical water extraction on soil properties was measured the investigation of the processes occurring within soil under the influence the high temperature and pressure. Under appropriate conditions of the experiment there is the destruction of the soil organic matter while the composition of the soil mineral fraction remains practically unchanged.

Proposed sub-criticality level for an 80 MWTHd-bismuth-cooled Ads

International Nuclear Information System (INIS)

Mansani, L.; Monti, R.; Neuhold, P.

2003-01-01

The degree of operational sub-criticality of an Accelerator-driven System (ADS) on the one hand directly affects key accelerator system parameters, such as the proton beam current required to sustain the selected rated power level and, on the other, the likelihood of approaching or attaining criticality under abnormal or accident conditions. Then, if in all such conditions the safety goal is pursued to design the sub-critical core so that it stays away from criticality with adequate margin, the required operational sub-criticality level must be determined by a properly balanced approach between excessively demanding accelerator system performances and risk of accidental criticality. The approach must necessarily include evaluation and appropriate combination of the relevant reactivity effects (e.g. from system cool-down, postulated accident scenarios, geometrical variations) and proper consideration of specific design features (such as, for instance, the absence of safety rods, intended as neutron absorbing devices having a role equivalent to the shutdown rods in critical reactors). The paper presents a possible approach to the determination of the operational sub-criticality level of an 80 MWth Lead-Bismuth-cooled pool type ADS, initially conceived and developed by a team of Italian Organisations led by Ansaldo, with funding from the Ministry of University and Scientific and Technological Research, and currently in the process of being assessed, versus a gas-cooled concept, in the frame of a contract with the Commission of the European Communities. After a brief description of the Lead-Bismuth-cooled ADS concept relevant features and of the key safety goals in terms of required sub-criticality margin, the evaluated reactivity effects are presented, a method to combine them is discussed and a proposed operational sub-criticality level is derived. (author)

The Dynamical Behaviors for a Class of Immunogenic Tumor Model with Delay

Directory of Open Access Journals (Sweden)

Ping Bi

2017-01-01

Full Text Available This paper aims at studying the model proposed by Kuznetsov and Taylor in 1994. Inspired by Mayer et al., time delay is introduced in the general model. The dynamic behaviors of this model are studied, which include the existence and stability of the equilibria and Hopf bifurcation of the model with discrete delays. The properties of the bifurcated periodic solutions are studied by using the normal form on the center manifold. Numerical examples and simulations are given to illustrate the bifurcation analysis and the obtained results.

Bistable Chimera Attractors on a Triangular Network of Oscillator Populations

DEFF Research Database (Denmark)

Martens, Erik Andreas

2010-01-01

. This triangular network is the simplest discretization of a continuous ring of oscillators. Yet it displays an unexpectedly different behavior: in contrast to the lone stable chimera observed in continuous rings of oscillators, we find that this system exhibits two coexisting stable chimeras. Both chimeras are......, as usual, born through a saddle-node bifurcation. As the coupling becomes increasingly local in nature they lose stability through a Hopf bifurcation, giving rise to breathing chimeras, which in turn get destroyed through a homoclinic bifurcation. Remarkably, one of the chimeras reemerges by a reversal...

Dedicated bifurcation stents

Directory of Open Access Journals (Sweden)

Ajith Ananthakrishna Pillai

2012-03-01

Full Text Available Bifurcation percutaneous coronary intervention (PCI is still a difficult call for the interventionist despite advancements in the instrumentation, technical skill and the imaging modalities. With major cardiac events relate to the side-branch (SB compromise, the concept and practice of dedicated bifurcation stents seems exciting. Several designs of such dedicated stents are currently undergoing trials. This novel concept and pristine technology offers new hope notwithstanding the fact that we need to go a long way in widespread acceptance and practice of these gadgets. Some of these designs even though looks enterprising, the mere complex delivering technique and the demanding knowledge of the exact coronary anatomy makes their routine use challenging.

Design project of fast subcritical system 'Mala Lasta'; Idejno resenje brzog podkriticnog sistema Mala LASTA

Energy Technology Data Exchange (ETDEWEB)

Milosevic, M; Stefanovic, D; Popovic, D; Pesic, M; Zavaljevski, N; Nikolic, D; Arsenovic, M [Boris Kidric Institute of nuclear sciences Vinca, Belgrade (Yugoslavia)

1988-10-15

This report contains two parts. Part one covers the objective and fundamental elements for the choice of fast subcritical system 'Mala Lasta', review of the existing fast subcritical assemblies, and a description of the available domestic computer codes applied for calculating neutron reactor parameters. Comparison of results obtained by these codes for a number of existing subcritical assemblies was used for the choice of the design project described in part two of this report. It contains detailed description of the operating parameters of the chosen subcritical system based on the obtained calculated parameters.

Subcritical Noise Analysis Measurements with Fresh and Spent Research Reactor Fuels Elements

International Nuclear Information System (INIS)

Valentine, T.E.; Mihalczo, J.T.; Kryter, R.C.; Miller, V.C.

1999-01-01

The verification of the subcriticality is of utmost importance for the safe transportation and storage of nuclear reactor fuels. Transportation containers and storage facilities are designed such that nuclear fuels remain in a subcritical state. Such designs often involve excess conservatism because of the lack of relevant experimental data to verify the accuracy of Monte Carlo codes used in nuclear criticality safety analyses. A joint experimental research program between Oak Ridge National Laboratory, Westinghouse Safety Management Solutions, Inc., and the University of Missouri was initiated to obtain measured quantities that could be directly related to the subcriticality of simple arrays of Missouri University Research Reactor (MURR) fuel elements. A series of measurement were performed to assess the reactivity of materials such as BORAL, stainless steel, aluminum, and lead that are typically used in the construction of shipping casks. These materials were positioned between the fuel elements. In addition, a limited number of measurements were performed with configurations of fresh and spent (irradiated) fuel elements to ascertain the reactivity of the spent fuel elements. In these experiments, fresh fuel elements were replaced by spent fuel elements such that the subcritical reactivity change could be measured. The results of these measurements were used by Westinghouse Safety Management Solutions to determine the subcriticality of MURR fuel elements isolated by absorbing materials. The measurements were interpreted using the MCNP-DSP Monte Carlo code to obtain the subcritical neutron multiplication factor k(sub eff), and the bias in K(sub eff) that are used in criticality safety analyses

Critical bifurcation surfaces of 3D discrete dynamics

Directory of Open Access Journals (Sweden)

Michael Sonis

2000-01-01

Full Text Available This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of the n-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.

Resonant Homoclinic Flips Bifurcation in Principal Eigendirections

Directory of Open Access Journals (Sweden)

Tiansi Zhang

2013-01-01

Full Text Available A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the Poincaré return map and the bifurcation equation. A detailed investigation produces the number and the existence of 1-homoclinic orbit, 1-periodic orbit, and double 1-periodic orbits. We also locate their bifurcation surfaces in certain regions.

Influence of surrounding environment on subcritical crack growth in marble

Science.gov (United States)

Nara, Yoshitaka; Kashiwaya, Koki; Nishida, Yuki; , Toshinori, Ii

2017-06-01

Understanding subcritical crack growth in rock is essential for determining appropriate measures to ensure the long-term integrity of rock masses surrounding structures and for construction from rock material. In this study, subcritical crack growth in marble was investigated experimentally, focusing on the influence of the surrounding environment on the relationship between the crack velocity and stress intensity factor. The crack velocity increased with increasing temperature and/or relative humidity. In all cases, the crack velocity increased with increasing stress intensity factor. However, for Carrara marble (CM) in air, we observed a region in which the crack velocity still increased with temperature, but the increase in the crack velocity with increasing stress intensity factor was not significant. This is similar to Region II of subcritical crack growth observed in glass in air. Region II in glass is controlled by mass transport to the crack tip. In the case of rock, the transport of water to the crack tip is important. In general, Region II is not observed for subcritical crack growth in rock materials, because rocks contain water. Because the porosity of CM is very low, the amount of water contained in the marble is also very small. Therefore, our results imply that we observed Region II in CM. Because the crack velocity increased in both water and air with increasing temperature and humidity, we concluded that dry conditions at low temperature are desirable for the long-term integrity of a carbonate rock mass. Additionally, mass transport to the crack tip is an important process for subcritical crack growth in rock with low porosity.

Burning of spent fuel of an accelerator-driven modular HTGR in sub-critical condition

International Nuclear Information System (INIS)

Jing Xingqing; Yang Yongwei; Chang Hong; Wu Zongxin; Gu Yuxiang

2002-01-01

The modular high temperature gas cooled reactor (MHTGR) has good safety characteristics because of the use of coated particles in the fuel element. After the particles cool outside of the reactor for some time, the spent fuel can be re-utilized. The author describes a physics feasibility study for the burning of spent fuel from a 350 MW ring-shaped modular high temperature gas cooled reactor in an accelerator-driven sub-critical reactor. A conceptual design is given for the 30 MW accelerator-driven sub-critical reactor. The neutron transport in the sub-critical reactor was simulated using the MCNP code, and the burnup was calculated using the ORIGEN2 code. The results show that the accelerator-driven sub-critical gas-cooled reactor has reliable sub-criticality and low power density and that the spent fuel from a 350 MW ring-shaped modular high temperature gas cooled reactor can be burned to provide 20% more energy

Development of High Flux Isotope Reactor (HFIR) subcriticality monitoring methods

International Nuclear Information System (INIS)

Rothrock, R.B.

1991-01-01

Use of subcritical source multiplication measurements during refueling has been investigated as a possible replacement for out-of-reactor subcriticality measurements formerly made on fresh HFIR fuel elements at the ORNL Critical Experiment Facility. These measurements have been used in the past for preparation of estimated critical rod positions, and as a partial verification, prior to reactor startup, that the requirements for operational shutdown margin would be met. Results of subcritical count rate data collection during recent HFIR refuelings and supporting calculations are described illustrating the intended measurement method and its expected uncertainty. These results are compared to historical uses of the out-of-reactor core measurements and their accuracy requirements, and a planned in-reactor test is described which will establish the sensitivity of the method and calibrate it for future routine use during HFIR refueling. 2 refs., 1 fig., 2 tabs

Discriminators for the Accelerator-Based Conversion (ABC) concept using a subcritical molten salt system

International Nuclear Information System (INIS)

Arthur, E.; Busksa, J.; Davidson, W.; Poston, D.

1995-05-01

Discriminators are described that quantify enhancements added to plutonium destruction and/or nuclear waste transmutation systems through use of an accelerator/fluid fuel combination. This combination produces a robust and flexible nuclear system capable of the destruction of all major long-lived actinides (including plutonium) and fission products. The discriminators discussed in this report are (1) impact of subcritical operation on safety, (2) impact of subcritical and fluid fuel operation on plutonium burnout scenarios, and (3) neutron economy enhancements brought about by subcritical operation. Neutron economy enhancements are quantified through assessment of long-term dose reduction resulting from transmutation of key fission products along with relaxation of processing frequencies afforded by subcritical operation

Estimation of subcriticality with the computed values. 2

Energy Technology Data Exchange (ETDEWEB)

Sakurai, Kiyoshi; Arakawa, Takuya; Naito, Yoshitaka [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment

1996-02-01

For measurements of reactivities and neutron count rate space distributions, seven subcritical cores including non-square array cores were constructed using critical assembly TCA. MCNP-4A was used for the experimental analysis. The calculational results of the neutron count rate space distributions agreed with the measured ones within the each error range. It means that for calculation error indirect estimation method, the calculated neutron multiplication factors are equal to ones of experimental reactivities. It is shown that from these experiments and calculations estimation method of subcriticality with the computed values based on the calculation error indirect estimation method is also applicable to six non-square array cores. (author).

ITEP Subcritical Neutron Generator driven by charged particle accelerator

Energy Technology Data Exchange (ETDEWEB)

Shvedov, O.V.; Chuvilo, I.V.; Vasiliev, V.V. [Institute of Theoretical and Experimental Physics, Moscow (Russian Federation)] [and others

1995-10-01

A research facility prototype including a combination of a linear accelerator, a neutron generating target, a nuclear safety ensuring and means of its attainment for Subcritical Neutron Generator are considered. The scheme of the multiplying is shown. The assembly will be mounted in the body of the partly dismantled ITEP HWR. Requirements for subcritical assembly are worked out and their feasibility within the framework of the heavy-water blanket is shown. The facility`s application as a full-scale model of more powerful installations of this kind and for fundamental experimental research has been investigated.

Periodic and chaotic oscillations in a tumor and immune system interaction model with three delays

International Nuclear Information System (INIS)

Bi, Ping; Ruan, Shigui; Zhang, Xinan

2014-01-01

In this paper, a tumor and immune system interaction model consisted of two differential equations with three time delays is considered in which the delays describe the proliferation of tumor cells, the process of effector cells growth stimulated by tumor cells, and the differentiation of immune effector cells, respectively. Conditions for the asymptotic stability of equilibria and existence of Hopf bifurcations are obtained by analyzing the roots of a second degree exponential polynomial characteristic equation with delay dependent coefficients. It is shown that the positive equilibrium is asymptotically stable if all three delays are less than their corresponding critical values and Hopf bifurcations occur if any one of these delays passes through its critical value. Numerical simulations are carried out to illustrate the rich dynamical behavior of the model with different delay values including the existence of regular and irregular long periodic oscillations

Workshop on Subcritical Neutron Production

International Nuclear Information System (INIS)

Walter Sadowski; Roald Sagdeev

2006-01-01

Executive Summary of the Workshop on Subcritical Neutron Production A workshop on Subcritical Neutron Production was sponsored by the East-West Center of the University of Maryland on October 11-13, 2004. The subject of the workshop was the application of subcritical neutrons to transmutation of actinides. The workshop was attended by members of the fission, accelerator and fusion communities. Papers on the state of development of neutron production by accelerators, fusion devices, and fission reactors were presented. Discussions were held on the potential of these technologies to solve the problems of spent nuclear waste storage and nuclear non-proliferation presented by current and future nuclear power reactors. A list of participants including their affiliation and their E-Mail addresses is attached. The workshop concluded that the technologies, presently available or under development, hold out the exciting possibility of improving the environmental quality and long term energy resources of nuclear power while strengthening proliferation resistance. The workshop participants agreed on the following statements. The workshop considered a number of technologies to deal with spent nuclear fuels and current actinide inventories. The conclusion was reached that substantial increase in nuclear power production will require that the issue of spent nuclear fuel be resolved. The Workshop concluded that 14 MeV fusion neutrons can be used to destroy nuclear reactor by-products, some of which would otherwise have to be stored for geologic periods of time. The production of 14 MeV neutrons is based on existing fusion technologies at different research institutions in several countries around the world. At the present time this technology is used to produce 14 MeV neutrons in JET. More development work will be required, however, to bring fusion technology to the level where it can be used for actinide burning on an industrial scale. The workshop concluded that the potential

Experimental determination of the neutron source for the Argonauta reactor subcritical assembly

Energy Technology Data Exchange (ETDEWEB)

Renke, Carlos A.C.; Furieri, Rosanne C.A.A.; Pereira, Joao C.S.; Voi, Dante L.; Barbosa, Andre L.N., E-mail: renke@ien.gov.b [Instituto de Engenharia Nuclear (IEN/CNEN-RJ), Rio de Janeiro, RJ (Brazil)

2011-07-01

The utilization of a subcritical assembly for the determination of nuclear parameters in a multiplier medium requires a well defined neutron source to carry out the experiments necessary for the acquisition of the desired data. The Argonauta research reactor installed at the Instituto de Engenharia Nuclear has a subcritical assembly, under development, to be coupled at the upper part of the reactor core that will provide the needed neutrons emerging from its internal thermal column made of graphite. In order to perform neutronic calculations to compare with the experimental results, it is necessary a precise knowledge of the emergent neutron flux that will be used as neutron source in the subcritical assembly. In this work, we present the thermal neutron flux profile determined experimentally via the technique of neutron activation analysis, using dysprosium wires uniformly distributed at the top of the internal thermal neutron column of the Argonauta reactor and later submitted to a detection system using Geiger-Mueller detector. These experimental data were then compared with those obtained through neutronic calculation using HAMMER and CITATION codes in order to validate this calculation system and to define a correct neutron source distribution to be used in the subcritical assembly. This procedure avoids a coupled neutronic calculation of the subcritical assembly and the reactor core. It has also been determined the dimension of the graphite pedestal to be used in the bottom of the subcritical assembly tank in order to smooth the emergent neutron flux at the reactor top. Finally, it is estimated the thermal neutron flux inside the assembly tank when filled with water. (author)

Local bifurcation analysis in nuclear reactor dynamics by Sotomayor’s theorem

International Nuclear Information System (INIS)

Pirayesh, Behnam; Pazirandeh, Ali; Akbari, Monireh

2016-01-01

Highlights: • When the feedback reactivity is considered as a nonlinear function some complex behaviors may emerge in the system such as local bifurcation phenomenon. • The qualitative behaviors of a typical nuclear reactor near its equilibrium points have been studied analytically. • Comprehensive analytical bifurcation analyses presented in this paper are transcritical bifurcation, saddle- node bifurcation and pitchfork bifurcation. - Abstract: In this paper, a qualitative approach has been used to explore nuclear reactor behaviors with nonlinear feedback. First, a system of four dimensional ordinary differential equations governing the dynamics of a typical nuclear reactor is introduced. These four state variables are the relative power of the reactor, the relative concentration of delayed neutron precursors, the fuel temperature and the coolant temperature. Then, the qualitative behaviors of the dynamical system near its equilibria have been studied analytically by using local bifurcation theory and Sotomayor’s theorem. The results indicated that despite the uncertainty of the reactivity, we can analyze the qualitative behavior changes of the reactor from the bifurcation point of view. Notably, local bifurcations that were considered in this paper include transcritical bifurcation, saddle-node bifurcation and pitchfork bifurcation. The theoretical analysis showed that these three types of local bifurcations may occur in the four dimensional dynamical system. In addition, to confirm the analytical results the numerical simulations are given.

Rich dynamics of a food chain model with ratio-dependent type III ...

African Journals Online (AJOL)

Rich dynamics of a food chain model with ratio-dependent type III functional responses. ... Stability analysis of model is carried out by using usual theory of ordinary ... that Hopf bifurcation may also occur when delay passes its critical value.

Pattern selection near the onset of convection in binary mixtures in cylindrical cells

International Nuclear Information System (INIS)

Alonso, Arantxa; Mercader, Isabel; Batiste, Oriol

2014-01-01

We report numerical investigations of three-dimensional pattern formation of binary mixtures in a vertical cylindrical container heated from below. Negative separation ratio mixtures, for which the onset of convection occurs via a subcritical Hopf bifurcation, are considered. We focus on the dynamics in the neighbourhood of the initial oscillatory instability and analyze the spatio-temporal properties of the patterns for different values of the aspect ratio of the cell, 0.25≲Γ≲11 (Γ≡R/d, where R is the radius of the cell and d its height). Despite the oscillatory nature of the primary instability, for highly constrained geometries, Γ≲2.5, only pure thermal stationary modes are selected after long transients. As the aspect ratio of the cell increases, for intermediate aspect ratio cells such as Γ=3, multistability and coexistence of stationary and time-dependent patterns is observed. In highly extended cylinders, Γ≈11, the dynamics near the onset is completely different from the pure fluid case, and a startling diversity of confined patterns is observed. Many of these patterns are consistent with experimental observations. Remarkably, though, we have obtained persistent large amplitude highly localized states not reported previously. (paper)

Pattern selection near the onset of convection in binary mixtures in cylindrical cells

Energy Technology Data Exchange (ETDEWEB)

Alonso, Arantxa; Mercader, Isabel; Batiste, Oriol, E-mail: arantxa@fa.upc.edu [Departament de Física Aplicada, Universitat Politècnica de Catalunya, Mòdul B4, 08034 Barcelona (Spain)

2014-08-01

We report numerical investigations of three-dimensional pattern formation of binary mixtures in a vertical cylindrical container heated from below. Negative separation ratio mixtures, for which the onset of convection occurs via a subcritical Hopf bifurcation, are considered. We focus on the dynamics in the neighbourhood of the initial oscillatory instability and analyze the spatio-temporal properties of the patterns for different values of the aspect ratio of the cell, 0.25≲Γ≲11 (Γ≡R/d, where R is the radius of the cell and d its height). Despite the oscillatory nature of the primary instability, for highly constrained geometries, Γ≲2.5, only pure thermal stationary modes are selected after long transients. As the aspect ratio of the cell increases, for intermediate aspect ratio cells such as Γ=3, multistability and coexistence of stationary and time-dependent patterns is observed. In highly extended cylinders, Γ≈11, the dynamics near the onset is completely different from the pure fluid case, and a startling diversity of confined patterns is observed. Many of these patterns are consistent with experimental observations. Remarkably, though, we have obtained persistent large amplitude highly localized states not reported previously. (paper)

Twist deformations leading to κ-Poincaré Hopf algebra and their application to physics

International Nuclear Information System (INIS)

Jurić, Tajron; Meljanac, Stjepan; Samsarov, Andjelo

2016-01-01

We consider two twist operators that lead to kappa-Poincaré Hopf algebra, the first being an Abelian one and the second corresponding to a light-like kappa-deformation of Poincaré algebra. The adventage of the second one is that it is expressed solely in terms of Poincaré generators. In contrast to this, the Abelian twist goes out of the boundaries of Poincaré algebra and runs into envelope of the general linear algebra. Some of the physical applications of these two different twist operators are considered. In particular, we use the Abelian twist to construct the statistics flip operator compatible with the action of deformed symmetry group. Furthermore, we use the light-like twist operator to define a star product and subsequently to formulate a free scalar field theory compatible with kappa-Poincaré Hopf algebra and appropriate for considering the interacting ϕ 4 scalar field model on kappa-deformed space. (paper)

Nonlinear analysis of a reaction-diffusion system: Amplitude equations

Energy Technology Data Exchange (ETDEWEB)

Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)

2012-10-15

A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.

Delay-Induced Oscillations in a Competitor-Competitor-Mutualist Lotka-Volterra Model

Directory of Open Access Journals (Sweden)

Changjin Xu

2017-01-01

Full Text Available This paper deals with a competitor-competitor-mutualist Lotka-Volterra model. A series of sufficient criteria guaranteeing the stability and the occurrence of Hopf bifurcation for the model are obtained. Several concrete formulae determine the properties of bifurcating periodic solutions by applying the normal form theory and the center manifold principle. Computer simulations are given to support the theoretical predictions. At last, biological meaning and a conclusion are presented.

Fluctuations in a mixed IS-LM business cycle model

Directory of Open Access Journals (Sweden)

Hamad Talibi Alaoui

2008-09-01

Full Text Available In the present paper, we extend a delayed IS-LM business cycle model by introducing an additional advance (anticipated capital stock in the investment function. The resulting model is represented in terms of mixed differential equations. For the deviating argument $au$ (advance and delay being a bifurcation parameter we investigate the local stability and the local Hopf bifurcation. Also some numerical simulations are given to support the theoretical analysis.

Bifurcation and instability problems in vortex wakes

DEFF Research Database (Denmark)

Aref, Hassan; Brøns, Morten; Stremler, Mark A.

2007-01-01

A number of instability and bifurcation problems related to the dynamics of vortex wake flows are addressed using various analytical tools and approaches. We discuss the bifurcations of the streamline pattern behind a bluff body as a vortex wake is produced, a theory of the universal Strouhal......-Reynolds number relation for vortex wakes, the bifurcation diagram for "exotic" wake patterns behind an oscillating cylinder first determined experimentally by Williamson & Roshko, and the bifurcations in topology of the streamlines pattern in point vortex streets. The Hamiltonian dynamics of point vortices...... in a periodic strip is considered. The classical results of von Kármán concerning the structure of the vortex street follow from the two-vortices-in-a-strip problem, while the stability results follow largely from a four-vortices-in-a-strip analysis. The three-vortices-in-a-strip problem is argued...

A Mechanistic Neural Field Theory of How Anesthesia Suppresses Consciousness: Synaptic Drive Dynamics, Bifurcations, Attractors, and Partial State Equipartitioning.

Science.gov (United States)

Hou, Saing Paul; Haddad, Wassim M; Meskin, Nader; Bailey, James M

2015-12-01

With the advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in understanding the molecular properties of anesthetic agents. However, there has been little focus on how the molecular properties of anesthetic agents lead to the observed macroscopic property that defines the anesthetic state, that is, lack of responsiveness to noxious stimuli. In this paper, we use dynamical system theory to develop a mechanistic mean field model for neural activity to study the abrupt transition from consciousness to unconsciousness as the concentration of the anesthetic agent increases. The proposed synaptic drive firing-rate model predicts the conscious-unconscious transition as the applied anesthetic concentration increases, where excitatory neural activity is characterized by a Poincaré-Andronov-Hopf bifurcation with the awake state transitioning to a stable limit cycle and then subsequently to an asymptotically stable unconscious equilibrium state. Furthermore, we address the more general question of synchronization and partial state equipartitioning of neural activity without mean field assumptions. This is done by focusing on a postulated subset of inhibitory neurons that are not themselves connected to other inhibitory neurons. Finally, several numerical experiments are presented to illustrate the different aspects of the proposed theory.

Solubility and degradation of paracetamol in subcritical water

Directory of Open Access Journals (Sweden)

Emire Zuhal

2017-01-01

Full Text Available In this study, solubility and degradation of paracetamol were examined using subcritical water. Effect of temperature and static time was investigated during solubility process in subcritical water at constant pressure (50 bar. Experimental results show that temperature and static time have crucial effect on the degradation and solubility rates. Maximum mole fraction for solubility of paracetamol was obtained at 403 K as (14.68 ± 0.74×103. Approximation model for solubility of paracetamol was proposed. O2 and H2O2 were used in degradation process of paracetamol. Maximum degradation rate was found as 68.66 ± 1.05 and 100 ± 0.00 % using O2 and H2O2, respectively.

Experimental subcritical facility driven by D-D/D-T neutron generator at BARC, India

Energy Technology Data Exchange (ETDEWEB)

Sinha, Amar, E-mail: image@barc.gov.in; Roy, Tushar; Kashyap, Yogesh; Ray, Nirmal; Shukla, Mayank; Patel, Tarun; Bajpai, Shefali; Sarkar, P.S.; Bishnoi, Saroj

2015-05-01

Highlights: •Experimental subcritical facility BRAHMMA coupled to D-D/D-T neutron generator. •Preliminary results of PNS experiments reported. •Feynman-alpha noise measurements explored with continuous source. -- Abstract: The paper presents design of an experimental subcritical assembly driven by D-D/D-T neutron and preliminary experimental measurements. The system has been developed for investigating the static and dynamic neutronic properties of accelerator driven sub-critical systems. This system is modular in design and it is first in the series of subcritical assemblies being designed. The subcritical core consists of natural uranium fuel with high density polyethylene as moderator and beryllium oxide as reflector. The fuel is embedded in high density polyethylene moderator matrix. Estimated k{sub eff} of the system is ∼0.89. One of the unique features of subcritical core is the use of Beryllium oxide (BeO) as reflector and HDPE as moderator making the assembly a compact modular system. The subcritical core is coupled to Purnima Neutron Generator which works in D-D and D-T mode with both DC and pulsed operation. It has facility for online source strength monitoring using neutron tagging and programmable source modulation. Preliminary experiments have been carried out for spatial flux measurement and reactivity estimation using pulsed neutron source (PNS) techniques with D-D neutrons. Further experiments are being planned to measure the reactivity and other kinetic parameters using noise methods. This facility would also be used for carrying out studies on effect of source importance and measurement of source multiplication factor k{sub s} and external neutron source efficiency φ{sup ∗} in great details. Experiments with D-T neutrons are also underway.

Stochastic bifurcation in a model of love with colored noise

Science.gov (United States)

Yue, Xiaokui; Dai, Honghua; Yuan, Jianping

2015-07-01

In this paper, we wish to examine the stochastic bifurcation induced by multiplicative Gaussian colored noise in a dynamical model of love where the random factor is used to describe the complexity and unpredictability of psychological systems. First, the dynamics in deterministic love-triangle model are considered briefly including equilibrium points and their stability, chaotic behaviors and chaotic attractors. Then, the influences of Gaussian colored noise with different parameters are explored such as the phase plots, top Lyapunov exponents, stationary probability density function (PDF) and stochastic bifurcation. The stochastic P-bifurcation through a qualitative change of the stationary PDF will be observed and bifurcation diagram on parameter plane of correlation time and noise intensity is presented to find the bifurcation behaviors in detail. Finally, the top Lyapunov exponent is computed to determine the D-bifurcation when the noise intensity achieves to a critical value. By comparison, we find there is no connection between two kinds of stochastic bifurcation.

Comments on the Bifurcation Structure of 1D Maps

DEFF Research Database (Denmark)

Belykh, V.N.; Mosekilde, Erik

1997-01-01

-within-a-box structure of the total bifurcation set. This presents a picture in which the homoclinic orbit bifurcations act as a skeleton for the bifurcational set. At the same time, experimental results on continued subharmonic generation for piezoelectrically amplified sound waves, predating the Feigenbaum theory......, are called into attention....

Predicting bifurcation angle effect on blood flow in the microvasculature.

Science.gov (United States)

Yang, Jiho; Pak, Y Eugene; Lee, Tae-Rin

2016-11-01

Since blood viscosity is a basic parameter for understanding hemodynamics in human physiology, great amount of research has been done in order to accurately predict this highly non-Newtonian flow property. However, previous works lacked in consideration of hemodynamic changes induced by heterogeneous vessel networks. In this paper, the effect of bifurcation on hemodynamics in a microvasculature is quantitatively predicted. The flow resistance in a single bifurcation microvessel was calculated by combining a new simple mathematical model with 3-dimensional flow simulation for varying bifurcation angles under physiological flow conditions. Interestingly, the results indicate that flow resistance induced by vessel bifurcation holds a constant value of approximately 0.44 over the whole single bifurcation model below diameter of 60μm regardless of geometric parameters including bifurcation angle. Flow solutions computed from this new model showed substantial decrement in flow velocity relative to other mathematical models, which do not include vessel bifurcation effects, while pressure remained the same. Furthermore, when applying the bifurcation angle effect to the entire microvascular network, the simulation results gave better agreements with recent in vivo experimental measurements. This finding suggests a new paradigm in microvascular blood flow properties, that vessel bifurcation itself, regardless of its angle, holds considerable influence on blood viscosity, and this phenomenon will help to develop new predictive tools in microvascular research. Copyright © 2016 Elsevier Inc. All rights reserved.

Accelerator-driven subcritical facility:Conceptual design development

Science.gov (United States)

Gohar, Yousry; Bolshinsky, Igor; Naberezhnev, Dmitry; Duo, Jose; Belch, Henry; Bailey, James

2006-06-01

A conceptual design development of an accelerator-driven subcritical facility has been carried out in the preparation of a joint activity with Kharkov Institute of Physics and Technology of Ukraine. The main functions of the facility are the medical isotope production and the support of the Ukraine nuclear industry. An electron accelerator is considered to drive the subcritical assembly. The neutron source intensity and spectrum have been studied. The energy deposition, spatial neutron generation, neutron utilization fraction, and target dimensions have been quantified to define the main target performance parameters, and to select the target material and beam parameters. Different target conceptual designs have been developed based the engineering requirements including heat transfer, thermal hydraulics, structure, and material issues. The subcritical assembly is designed to obtain the highest possible neutron flux level with a Keff of 0.98. Different fuel materials, uranium enrichments, and reflector materials are considered in the design process. The possibility of using low enrichment uranium without penalizing the facility performance is carefully evaluated. The mechanical design of the facility has been developed to maximize its utility and minimize the time for replacing the target and the fuel assemblies. Safety, reliability, and environmental considerations are included in the facility conceptual design. The facility is configured to accommodate future design improvements, upgrades, and new missions. In addition, it has large design margins to accommodate different operating conditions and parameters. In this paper, the conceptual design and the design analyses of the facility will be presented.

Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex Nonlinearity

Directory of Open Access Journals (Sweden)

Antonio Olivas Martinez

2009-01-01

Full Text Available We consider the Riemann problem for the Hopf equation with concave-convex flux functions. Applying the weak asymptotics method we construct a uniform in time description for the Cauchy data evolution and show that the use of this method implies automatically the appearance of the Oleinik E-condition.

Hopf-algebraic renormalization of QED in the linear covariant gauge

Energy Technology Data Exchange (ETDEWEB)

Kißler, Henry, E-mail: kissler@physik.hu-berlin.de

2016-09-15

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.

Defining Electron Bifurcation in the Electron-Transferring Flavoprotein Family.

Science.gov (United States)

Garcia Costas, Amaya M; Poudel, Saroj; Miller, Anne-Frances; Schut, Gerrit J; Ledbetter, Rhesa N; Fixen, Kathryn R; Seefeldt, Lance C; Adams, Michael W W; Harwood, Caroline S; Boyd, Eric S; Peters, John W

2017-11-01

Electron bifurcation is the coupling of exergonic and endergonic redox reactions to simultaneously generate (or utilize) low- and high-potential electrons. It is the third recognized form of energy conservation in biology and was recently described for select electron-transferring flavoproteins (Etfs). Etfs are flavin-containing heterodimers best known for donating electrons derived from fatty acid and amino acid oxidation to an electron transfer respiratory chain via Etf-quinone oxidoreductase. Canonical examples contain a flavin adenine dinucleotide (FAD) that is involved in electron transfer, as well as a non-redox-active AMP. However, Etfs demonstrated to bifurcate electrons contain a second FAD in place of the AMP. To expand our understanding of the functional variety and metabolic significance of Etfs and to identify amino acid sequence motifs that potentially enable electron bifurcation, we compiled 1,314 Etf protein sequences from genome sequence databases and subjected them to informatic and structural analyses. Etfs were identified in diverse archaea and bacteria, and they clustered into five distinct well-supported groups, based on their amino acid sequences. Gene neighborhood analyses indicated that these Etf group designations largely correspond to putative differences in functionality. Etfs with the demonstrated ability to bifurcate were found to form one group, suggesting that distinct conserved amino acid sequence motifs enable this capability. Indeed, structural modeling and sequence alignments revealed that identifying residues occur in the NADH- and FAD-binding regions of bifurcating Etfs. Collectively, a new classification scheme for Etf proteins that delineates putative bifurcating versus nonbifurcating members is presented and suggests that Etf-mediated bifurcation is associated with surprisingly diverse enzymes. IMPORTANCE Electron bifurcation has recently been recognized as an electron transfer mechanism used by microorganisms to maximize

Dynamic bifurcations on financial markets

International Nuclear Information System (INIS)

Kozłowska, M.; Denys, M.; Wiliński, M.; Link, G.; Gubiec, T.; Werner, T.R.; Kutner, R.; Struzik, Z.R.

2016-01-01

We provide evidence that catastrophic bifurcation breakdowns or transitions, preceded by early warning signs such as flickering phenomena, are present on notoriously unpredictable financial markets. For this we construct robust indicators of catastrophic dynamical slowing down and apply these to identify hallmarks of dynamical catastrophic bifurcation transitions. This is done using daily closing index records for the representative examples of financial markets of small and mid to large capitalisations experiencing a speculative bubble induced by the worldwide financial crisis of 2007-08.

Dynamic behavior of the bray-liebhafsky oscillatory reaction controlled by sulfuric acid and temperature

Science.gov (United States)

Pejić, N.; Vujković, M.; Maksimović, J.; Ivanović, A.; Anić, S.; Čupić, Ž.; Kolar-Anić, Lj.

2011-12-01

The non-periodic, periodic and chaotic regimes in the Bray-Liebhafsky (BL) oscillatory reaction observed in a continuously fed well stirred tank reactor (CSTR) under isothermal conditions at various inflow concentrations of the sulfuric acid were experimentally studied. In each series (at any fixed temperature), termination of oscillatory behavior via saddle loop infinite period bifurcation (SNIPER) as well as some kind of the Andronov-Hopf bifurcation is presented. In addition, it was found that an increase of temperature, in different series of experiments resulted in the shift of bifurcation point towards higher values of sulfuric acid concentration.

Pierce instability and bifurcating equilibria

International Nuclear Information System (INIS)

Godfrey, B.B.

1981-01-01

The report investigates the connection between equilibrium bifurcations and occurrence of the Pierce instability. Electrons flowing from one ground plane to a second through an ion background possess a countable infinity of static equilibria, of which only one is uniform and force-free. Degeneracy of the uniform and simplest non-uniform equilibria at a certain ground plan separation marks the onset of the Pierce instability, based on a newly derived dispersion relation appropriate to all the equilibria. For large ground plane separations the uniform equilibrium is unstable and the non-uniform equilibrium is stable, the reverse of their stability properties at small separations. Onset of the Pierce instability at the first bifurcation of equilibria persists in more complicated geometries, providing a general criterion for marginal stability. It seems probable that bifurcation analysis can be a useful tool in the overall study of stable beam generation in diodes and transport in finite cavities

Development study on subcriticality monitor. 1. Report under business contract with Japan Nuclear Fuel Cycle Development Institute

CERN Document Server

Yamada, S

2002-01-01

In this trust fund, we reviewed subcriticality measuring methods and neutron or gamma ray measuring and date transmission systems appropriate for realizing inexpensive on-line criticality surveillance systems, which is required for ensuring the safety of nuclear fuel reprocessing plants. Since the neutron flux level in subcritical systems is fairly low without external neutron sources, it is desirable to use pulse type neutron detectors for subcritical measurement systems. This logically implies that subcriticality measurement methods based on the temporal domain should be used for developing an on-line criticality surveillance system. In the deep subcriticality conditions, a strong external neutron source is needed for eactivity measurement and a D-T tube can be used in order to improve the accuracy of the measurement. A D-T tube is convenient since it is free from Tritium problem since Tritium is sealed in an airtight container and also can be controlled by power supply. Hence, under deep subcritical condit...

The safe, economical operation of a slightly subcritical reactor and transmutor with a small proton accelerator

International Nuclear Information System (INIS)

Takahashi, Hiroshi

1994-01-01

I suggest that an accelerator can be used to increase the safety and neutron economy of a power reactor and a transmutor of long-lived radioactive wastes, such as minor actinides and fission products, by providing neutrons for its subcritical operation. Instead of the large subcriticality k=0.9-0.95 which we originally proposed for such transmutor, we propose to use a slightly subcritical reactor, such as k=0.99, which will avoid many of the technical difficulties that are associated with large subcriticality, such as localized power peaking, radiation damage due to injection of medium-energy protons, the high current accelerator, and the requirement for a long beam-expansion section. We analyze the power drop that occurred in Phenix reactor, and show that the operating this reactor in subcritical conditions improves safety. (author). 13 refs., 5 figs

The safe, economical operation of a slightly subcritical reactor and transmutor with a small proton accelerator

International Nuclear Information System (INIS)

Takahashi, Hiroshi.

1994-01-01

This report describes methods in which an accelerator can be used to increase the safety and neutron economy of a power reactor and transmutor of long-lived radioactive wastes, such as minor actinides and fission products, by providing neutrons for its subcritical operation. Instead of the rather large subcriticality of k=0.9--0.95 which we originally proposed for such a transmutor, we propose to use a slightly subcritical reactor, such as k=0.99, which will avoid many of the technical difficulties that are associated with large subcriticality, such as localized power peaking, radiation damage due to the injection of medium-energy protons, the high current accelerator, and the requirement for a long beam-expansion section. We analyzed the power drop that occurred in Phoenix reactor, and show that the operating this reactor in subcritical condition improves its safety

Bifurcations of optimal vector fields: an overview

NARCIS (Netherlands)

Kiseleva, T.; Wagener, F.; Rodellar, J.; Reithmeier, E.

2009-01-01

We develop a bifurcation theory for the solution structure of infinite horizon optimal control problems with one state variable. It turns out that qualitative changes of this structure are connected to local and global bifurcations in the state-costate system. We apply the theory to investigate an

Bifurcations of transition states: Morse bifurcations

International Nuclear Information System (INIS)

MacKay, R S; Strub, D C

2014-01-01

A transition state for a Hamiltonian system is a closed, invariant, oriented, codimension-2 submanifold of an energy level that can be spanned by two compact codimension-1 surfaces of unidirectional flux whose union, called a dividing surface, locally separates the energy level into two components and has no local recrossings. For this to happen robustly to all smooth perturbations, the transition state must be normally hyperbolic. The dividing surface then has locally minimal geometric flux through it, giving an upper bound on the rate of transport in either direction. Transition states diffeomorphic to S 2m−3 are known to exist for energies just above any index-1 critical point of a Hamiltonian of m degrees of freedom, with dividing surfaces S 2m−2 . The question addressed here is what qualitative changes in the transition state, and consequently the dividing surface, may occur as the energy or other parameters are varied? We find that there is a class of systems for which the transition state becomes singular and then regains normal hyperbolicity with a change in diffeomorphism class. These are Morse bifurcations. Various examples are considered. Firstly, some simple examples in which transition states connect or disconnect, and the dividing surface may become a torus or other. Then, we show how sequences of Morse bifurcations producing various interesting forms of transition state and dividing surface are present in reacting systems, by considering a hypothetical class of bimolecular reactions in gas phase. (paper)

Regularization of the Boundary-Saddle-Node Bifurcation

Directory of Open Access Journals (Sweden)

Xia Liu

2018-01-01

Full Text Available In this paper we treat a particular class of planar Filippov systems which consist of two smooth systems that are separated by a discontinuity boundary. In such systems one vector field undergoes a saddle-node bifurcation while the other vector field is transversal to the boundary. The boundary-saddle-node (BSN bifurcation occurs at a critical value when the saddle-node point is located on the discontinuity boundary. We derive a local topological normal form for the BSN bifurcation and study its local dynamics by applying the classical Filippov’s convex method and a novel regularization approach. In fact, by the regularization approach a given Filippov system is approximated by a piecewise-smooth continuous system. Moreover, the regularization process produces a singular perturbation problem where the original discontinuous set becomes a center manifold. Thus, the regularization enables us to make use of the established theories for continuous systems and slow-fast systems to study the local behavior around the BSN bifurcation.

Codimension-Two Bifurcation Analysis in DC Microgrids Under Droop Control

Science.gov (United States)

Lenz, Eduardo; Pagano, Daniel J.; Tahim, André P. N.

This paper addresses local and global bifurcations that may appear in electrical power systems, such as DC microgrids, which recently has attracted interest from the electrical engineering society. Most sources in these networks are voltage-type and operate in parallel. In such configuration, the basic technique for stabilizing the bus voltage is the so-called droop control. The main contribution of this work is a codimension-two bifurcation analysis of a small DC microgrid considering the droop control gain and the power processed by the load as bifurcation parameters. The codimension-two bifurcation set leads to practical rules for achieving a robust droop control design. Moreover, the bifurcation analysis also offers a better understanding of the dynamics involved in the problem and how to avoid possible instabilities. Simulation results are presented in order to illustrate the bifurcation analysis.

Solvable model for chimera states of coupled oscillators.

Science.gov (United States)

Abrams, Daniel M; Mirollo, Rennie; Strogatz, Steven H; Wiley, Daniel A

2008-08-22

Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized subpopulations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain the first exact results about the stability, dynamics, and bifurcations of chimera states by analyzing a minimal model consisting of two interacting populations of oscillators. Along with a completely synchronous state, the system displays stable chimeras, breathing chimeras, and saddle-node, Hopf, and homoclinic bifurcations of chimeras.

A model of a fishery with fish stock involving delay equations.

Science.gov (United States)

Auger, P; Ducrot, Arnaud

2009-12-13

The aim of this paper is to provide a new mathematical model for a fishery by including a stock variable for the resource. This model takes the form of an infinite delay differential equation. It is mathematically studied and a bifurcation analysis of the steady states is fulfilled. Depending on the different parameters of the problem, we show that Hopf bifurcation may occur leading to oscillating behaviours of the system. The mathematical results are finally discussed.

A Geometric Problem and the Hopf Lemma. Ⅱ

Institute of Scientific and Technical Information of China (English)

YanYan LI; Louis NIRENBERG

2006-01-01

A classical result of A. D. Alexandrov states that a connected compact smooth n-dimensional manifold without boundary, embedded in Rn+1, and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of M in a hyperplane Xn+1 =constant in case M satisfies: for any two points (X′, Xn+1), (X′, ^Xn+1)on M, with Xn+1 ＞ ^Hn+1, the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper, we establish it under some additional conditions. Some variations of the Hopf Lemma are also presented. Several open problems are described. Part Ⅰ dealt with corresponding one dimensional problems.

Inverse kinetics for subcritical systems with external neutron source

International Nuclear Information System (INIS)

Carvalho Gonçalves, Wemerson de; Martinez, Aquilino Senra; Carvalho da Silva, Fernando

2017-01-01

Highlights: • It was developed formalism for reactivity calculation. • The importance function is related to the system subcriticality. • The importance function is also related with the value of the external source. • The equations were analyzed for seven different levels of sub criticality. • The results are physically consistent with others formalism discussed in the paper. - Abstract: Nuclear reactor reactivity is one of the most important properties since it is directly related to the reactor control during the power operation. This reactivity is influenced by the neutron behavior in the reactor core. The time-dependent neutrons behavior in response to any change in material composition is important for the reactor operation safety. Transient changes may occur during the reactor startup or shutdown and due to accidental disturbances of the reactor operation. Therefore, it is very important to predict the time-dependent neutron behavior population induced by changes in neutron multiplication. Reactivity determination in subcritical systems driven by an external neutron source can be obtained through the solution of the inverse kinetics equation for subcritical nuclear reactors. The main purpose of this paper is to find the solution of the inverse kinetics equation the main purpose of this paper is to device the inverse kinetics equations for subcritical systems based in a previous paper published by the authors (Gonçalves et al., 2015) and by (Gandini and Salvatores, 2002; Dulla et al., 2006). The solutions of those equations were also obtained. Formulations presented in this paper were tested for seven different values of k eff with external neutrons source constant in time and for a powers ratio varying exponentially over time.

Oscillatory Stability and Eigenvalue Sensitivity Analysis of A DFIG Wind Turbine System

DEFF Research Database (Denmark)

Yang, Lihui; Xu, Zhao; Østergaard, Jacob

2011-01-01

This paper focuses on modeling and oscillatory stability analysis of a wind turbine with doubly fed induction generator (DFIG). A detailed mathematical model of DFIG wind turbine with vector-control loops is developed, based on which the loci of the system Jacobian's eigenvalues have been analyzed......, showing that, without appropriate controller tuning a Hopf bifurcation can occur in such a system due to various factors, such as wind speed. Subsequently, eigenvalue sensitivity with respect to machine and control parameters is performed to assess their impacts on system stability. Moreover, the Hopf...

On the Hopf structure of Up,q(gl(1/1)) and the universal Τ-matrix of Funp,q(GL(1/1))

International Nuclear Information System (INIS)

Chakrabarti, R.; Jagannathan, R.

1994-08-01

Using the technique developed by Fronsdal and Galindo (Lett. Math. Phys, 27 (1993) 57) for studying the Hopf duality between the quantum algebras Fun p,q (GL(2)) and U p,q (gl(2)), the Hopf structure of U p,q (gl(1/1)), dual to Fun p,q (GL(1/1)), is derived and the corresponding universal Τ-matrix of Fun p,q (GL(1/1)), embodying the suitably modified exponential relationship U p,q (gl(1/1)) → Fun p,q (GL(1/1)), is obtained. (author). 10 refs

Bifurcation of transition paths induced by coupled bistable systems.

Science.gov (United States)

Tian, Chengzhe; Mitarai, Namiko

2016-06-07

We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example and show that its transition paths are bifurcating. We then derive a criterion to predict the bifurcation of transition paths in a generalized coupled bistable system. We confirm the validity of the theory for the example system by numerical simulation. We also demonstrate in the example system that, if the steady states of individual gene circuits are not changed by the coupling, the bifurcation pattern is not dependent on the number of gene circuits. We further show that the transition rate exponentially decreases with the number of gene circuits when the transition path does not bifurcate, while a bifurcation facilitates the transition by lowering the quasi-potential energy barrier.

Feasibility of waste transmutation using accelerator-driven IRIS subcritical system

International Nuclear Information System (INIS)

Petroviae, B.; Carelli, M.; Paramonov, D.

2001-01-01

Waste transmutation is considered for reducing radio-toxicity of nuclear waste generated in power reactors. Accelerator driven subcritical systems (ADS) offer certain advantages over the use of nuclear reactors. Transmutation of fission products (e.g. 99 Tc) generally requires thermal neutron spectrum, while for actinides fast spectrum provides better performance. Proposed solutions to this problem include a multi-strata approach as well as a multi-zone (thermal/fast-spectrum) single systems. In this paper we examine the feasibility of employing a dual-spectrum two-zone accelerator-driven IRIS subcritical for waste transmutation. (author)

Percutaneous coronary intervention for the left main stem and other bifurcation lesions: 12th consensus document from the European Bifurcation Club.

Science.gov (United States)

Lassen, Jens Flensted; Burzotta, Francesco; Banning, Adrian P; Lefèvre, Thierry; Darremont, Olivier; Hildick-Smith, David; Chieffo, Alaide; Pan, Manuel; Holm, Niels Ramsing; Louvard, Yves; Stankovic, Goran

2018-01-20

The European Bifurcation Club (EBC) was initiated in 2004 to support a continuous overview of the field of coronary artery bifurcation interventions and aims to facilitate a scientific discussion and an exchange of ideas on the management of bifurcation disease. The EBC hosts an annual, two-day compact meeting, dedicated to bifurcations, which brings together physicians, pathologists, engineers, biologists, physicists, mathematicians, epidemiologists and statisticians for detailed discussions. Every meeting is finalised with a consensus statement that reflects the unique opportunity of combining the opinion of interventional cardiologists with the opinion of a large variety of other scientists on bifurcation management. A series of consensus sessions dedicated to specific topics, to strengthen the consensus debates and focus the discussions, was introduced at this year's meeting. The sessions comprise an intensive overview of the present literature, a pro and con debate and a voting system, to guide the consensus-building process. The present document represents the summary of the up-to-date EBC consensus and recommendations from the 12th annual EBC meeting in 2016 in Rotterdam.

Nonlinear physical systems spectral analysis, stability and bifurcations

CERN Document Server

Kirillov, Oleg N

2013-01-01

Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam

Fractional noise destroys or induces a stochastic bifurcation

Energy Technology Data Exchange (ETDEWEB)

Yang, Qigui, E-mail: qgyang@scut.edu.cn [School of Sciences, South China University of Technology, Guangzhou 510640 (China); Zeng, Caibin, E-mail: zeng.cb@mail.scut.edu.cn [School of Sciences, South China University of Technology, Guangzhou 510640 (China); School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China); Wang, Cong, E-mail: wangcong@scut.edu.cn [School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640 (China)

2013-12-15

Little seems to be known about the stochastic bifurcation phenomena of non-Markovian systems. Our intention in this paper is to understand such complex dynamics by a simple system, namely, the Black-Scholes model driven by a mixed fractional Brownian motion. The most interesting finding is that the multiplicative fractional noise not only destroys but also induces a stochastic bifurcation under some suitable conditions. So it opens a possible way to explore the theory of stochastic bifurcation in the non-Markovian framework.

Spontaneous symmetry breaking due to the trade-off between attractive and repulsive couplings.

Science.gov (United States)

Sathiyadevi, K; Karthiga, S; Chandrasekar, V K; Senthilkumar, D V; Lakshmanan, M

2017-04-01

Spontaneous symmetry breaking is an important phenomenon observed in various fields including physics and biology. In this connection, we here show that the trade-off between attractive and repulsive couplings can induce spontaneous symmetry breaking in a homogeneous system of coupled oscillators. With a simple model of a system of two coupled Stuart-Landau oscillators, we demonstrate how the tendency of attractive coupling in inducing in-phase synchronized (IPS) oscillations and the tendency of repulsive coupling in inducing out-of-phase synchronized oscillations compete with each other and give rise to symmetry breaking oscillatory states and interesting multistabilities. Further, we provide explicit expressions for synchronized and antisynchronized oscillatory states as well as the so called oscillation death (OD) state and study their stability. If the Hopf bifurcation parameter (λ) is greater than the natural frequency (ω) of the system, the attractive coupling favors the emergence of an antisymmetric OD state via a Hopf bifurcation whereas the repulsive coupling favors the emergence of a similar state through a saddle-node bifurcation. We show that an increase in the repulsive coupling not only destabilizes the IPS state but also facilitates the reentrance of the IPS state.

Prey-predator dynamics with prey refuge providing additional food to predator

International Nuclear Information System (INIS)

Ghosh, Joydev; Sahoo, Banshidhar; Poria, Swarup

2017-01-01

Highlights: • The effects of interplay between prey refugia and additional food are reported. • Hopf bifurcation conditions are derived analytically. • Existence of unique limit cycle is shown analytically. • Predator extinction may be possible at very high prey refuge ecological systems. - Abstract: The impacts of additional food for predator on the dynamics of a prey-predator model with prey refuge are investigated. The equilibrium points and their stability behaviours are determined. Hopf bifurcation conditions are derived analytically. Most significantly, existence conditions for unique stable limit cycle in the phase plane are shown analytically. The analytical results are in well agreement with the numerical simulation results. Effects of variation of refuge level as well as the variation of quality and quantity of additional food on the dynamics are reported with the help of bifurcation diagrams. It is found that high quality and high quantity of additional food supports oscillatory coexistence of species. It is observed that predator extinction possibility in high prey refuge ecological systems may be removed by supplying additional food to predator population. The reported theoretical results may be useful to conservation biologist for species conservation in real world ecological systems.

Cost optimization of ADS design: Comparative study of externally driven heterogeneous and homogeneous two-zone subcritical reactor systems

International Nuclear Information System (INIS)

Gulik, Volodymyr; Tkaczyk, Alan H.

2014-01-01

Highlights: • The optimization of two-zone homogeneous subcritical systems has been performed. • A Serpent model for two-zone heterogeneous subcritical systems has been developed. • The optimization of two-zone heterogeneous subcritical systems has been carried out. • Economically optimal core composition of two-zone subcritical system was found. • The neutron spectra of the heterogeneous subcritical systems have been obtained. - Abstract: Subcritical systems driven by external neutron sources, commonly known as Accelerator-Driven System (ADS), are one type of advanced nuclear reactor exhibiting attractive characteristics, distinguished from the traditional critical systems by their intrinsic safety features. In addition, an ADS can be used for the transmutation of the nuclear waste, accumulated during the operation of existing reactors. The optimization of a subcritical nuclear reactor in terms of materials (fuel content, coolant, etc.), geometrical, and economical parameters is a crucial step in the process of their design and construction. This article describes the optimization modeling performed for homogeneous and heterogeneous two-zone subcritical systems in terms of geometry of the fuel zones. Economical assessment was also carried out for the costs of the fuel in the core of the system. Optimization modeling was performed with the Serpent-1.1.18 Monte Carlo code. The model of a two-zone subcritical system with a fast inner and a thermal gas-cooled graphite-moderated outer zone was developed, simulated, and analyzed. The optimal value for the pitch of fuel elements in the thermal outer zone was investigated from the viewpoint of the cost of subcritical system. As the main goal of ADS development is nuclear waste transmutation, neutron spectra for both fast and thermal zones were obtained for different system configurations. The results of optimization modeling of homogeneous and heterogeneous two-zone subcritical systems show that an optimal

A microfluidic sub-critical water extraction instrument

Science.gov (United States)

Sherrit, Stewart; Noell, Aaron C.; Fisher, Anita; Lee, Mike C.; Takano, Nobuyuki; Bao, Xiaoqi; Kutzer, Thomas C.; Grunthaner, Frank

2017-11-01

This article discusses a microfluidic subcritical water extraction (SCWE) chip for autonomous extraction of amino acids from astrobiologically interesting samples. The microfluidic instrument is composed of three major components. These include a mixing chamber where the soil sample is mixed and agitated with the solvent (water), a subcritical water extraction chamber where the sample is sealed with a freeze valve at the chip inlet after a vapor bubble is injected into the inlet channels to ensure the pressure in the chip is in equilibrium with the vapor pressure and the slurry is then heated to ≤200 °C in the SCWE chamber, and a filter or settling chamber where the slurry is pumped to after extraction. The extraction yield of the microfluidic SCWE chip process ranged from 50% compared to acid hydrolysis and 80%-100% compared to a benchtop microwave SCWE for low biomass samples.

Production of rare sugars from common sugars in subcritical aqueous ethanol.

Science.gov (United States)

Gao, Da-Ming; Kobayashi, Takashi; Adachi, Shuji

2015-05-15

A new isomerization reaction was developed to synthesize rare ketoses. D-tagatose, D-xylulose, and D-ribulose were obtained in the maximum yields of 24%, 38%, and 40%, respectively, from the corresponding aldoses, D-galactose, D-xylose, and D-ribose, by treating the aldoses with 80% (v/v) subcritical aqueous ethanol at 180°C. The maximum productivity of D-tagatose was ca. 80 g/(Lh). Increasing the concentration of ethanol significantly increased the isomerization of D-galactose. Variation in the reaction temperature did not significantly affect the production of D-tagatose from D-galactose. Subcritical aqueous ethanol converted both 2,3-threo and 2,3-erythro aldoses to the corresponding C-2 ketoses in high yields. Thus, the treatment of common aldoses in subcritical aqueous ethanol can be regarded as a new method to synthesize the corresponding rare sugars. Copyright © 2014 Elsevier Ltd. All rights reserved.

Bifurcation of self-folded polygonal bilayers