Autonomous third-order duffing-holmes type chaotic oscillator
DEFF Research Database (Denmark)
Lindberg, Erik; Tamaseviciute, E; Mykolaitis, G
2009-01-01
A novel Duffing-Holmes type autonomous chaotic oscillator is described. In comparison with the well-known nonautonomous Duffing-Holmes circuit it lacks the external periodic drive, but includes two extra linear feedback subcircuits, namely a direct positive feedback loop, and an inertial negative...... feedback loop. In contrast to many other autonomous chaotic oscillators, including linear unstable resonators and nonlinear damping loops, the novel circuit is based on nonlinear resonator and linear damping loop in the negative feedback. SPICE simulation and hardware experimental investigations...... are presented. The Lyapunov exponents calculated from the rate equations confirm dynamical nature of chaotic oscillations....
Autonomous Duffing-Holmes Type Chaotic Oscillator
DEFF Research Database (Denmark)
Tamaševičius, A.; Bumelienė, S.; Kirvaitis, R.
2009-01-01
We have designed and built a novel Duffing type autonomous 3rd-order chaotic oscillator. In comparison with the common non-autonomous DuffingHolmes type oscillator the autonomous circuit has an internal positive feedback loop instead of an external periodic drive source. In addition...
Kengne, J.; Njitacke Tabekoueng, Z.; Fotsin, H. B.
2016-07-01
We perform a systematic analysis of a system consisting of an autonomous third order Duffing-Holmes type chaotic oscillator recently introduced by Tamasevicius et al. (2009). In this type of oscillators, the symmetrical characteristics of the nonlinear component necessary for generating chaotic oscillations is synthesized by using a pair of semiconductor diodes connected in anti-parallel. Based on the Shockley diode equation and a judicious choice of state variables, we derive a smooth mathematical model (involving hyperbolic sine and cosine functions) for a better description of both the regular and chaotic dynamics of the oscillator. The bifurcation analysis shows that chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. More interestingly, some regions of the parameter space corresponding to the coexistence of multiple attractors (e.g. coexistence of four different attractors for the same values of system parameters) are discovered. This striking phenomenon is unique and has not yet been reported previously in an electrical circuit (the universal Chua's circuit included, in spite the immense amount of related research work), and thus represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. Some PSpice simulations of the nonlinear dynamics of the oscillator are carried out to verify the theoretical analysis.
CHAOTIC DUFFING TYPE OSCILLATOR WITH INERTIAL DAMPING
DEFF Research Database (Denmark)
Tamaševicius, Arunas; Mykolaitis, Gytis; Kirvaitis, Raimundas
2009-01-01
A novel Duffing-Holmes type autonomous chaotic oscillator is described. In comparison with the well-known non-autonomous Duffing-Holmes circuit it lacks the external periodic drive, but includes two extra linear feedback sub-circuits, namely a direct positive feedback loop, and an inertial negative...
Institute of Scientific and Technical Information of China (English)
孙立莹; 周璇; 常志英
2012-01-01
通过对混沌振子Duffing-Holmes方程及其检测原理的介绍,发现混沌振子对周期小信号具有敏感特性,能够在强噪声环境下实现对微弱周期小信号的检测.Matlab实验仿真和分析证明了采用混沌振子Duffing-Holmes检测微弱周期小信号的可行性.%It is a find that chaotic oscillators is sensitive to faint periodic small signal by introduction about chaotic Duffing-Holmes equation and detection of theory, and it can detect the faint periodic small signal in strong noise background. It was indicted that the detection is feasible, make use of chaotic Duffing-Holmes equation by Matlab simulation result and analysis.
Analogue Electrical Circuit for Simulation of the Duffing-Holmes Equation
DEFF Research Database (Denmark)
Tamaseviciute, E.; Tamasevicius, A.; Mykolaitis, G.
2008-01-01
An extremely simple second order analogue electrical circuit for simulating the two-well Duffing-Holmes mathematical oscillator is described. Numerical results and analogue electrical simulations are illustrated with the snapshots of chaotic waveforms, phase portraits (Lissajous figures...
Chaotic system for the detection of periodic signals under the background of strong noise
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
We propose a method to study the chaotic system for the detection of periodic signals in the presence of strong background noise. The numerical experiments indicate that the chaotic system constructed from the modified Duffing-Holmes equation is sensitive to the weak periodic signal mixed with noise, and it has certain immunity to noise. The signal to noise ratio for the system can reach to about -91 dB.
Institute of Scientific and Technical Information of China (English)
Li Yue; Yang Bao-Jun; Deng Xiao-Ying; Jin Lei; Du Li-Zhi
2004-01-01
In the zero-order approximation, we use the perturbation method of parameter with small magnitude to prove that the harmonic frequency in the solution of the equation is close to that of the driving force when the chaotic system from Duffing-Holmes equation stays in the stable periodic state, which is the physical mechanism of the detection of the unknown frequency of weak harmonic signal using the chaotic theory. The result of the simulation experiment shows that the method proposed in this paper, by which one can determine the frequency of the stable system from the number of circulation change of the phase state directionally across a fixed phase state point (x, x) in fixed simulation time period, is successful. Analyzing the effects of the damping ratio on the chaotic detection result, one can see that for different frequency ranges it is necessary to carefully choose corresponding damping ratio α.
Generation and dynamics analysis of N-scrolls existence in new translation-type chaotic systems
Liu, Yue; Guo, Shuxu
2016-11-01
In this paper, we propose two kinds of translation type chaotic systems for creating 2 N + 1-and 2(N + 1)-scrolls chaotic attractors from a simple three-dimensional system, which are named the translation-2 chaotic system (a12a21 0). We also propose the successful design criterion for constructing 2 N + 1-and 2(N + 1)-scrolls, respectively. Then, the dynamics property of the translation-2 chaotic system is studied in detail. MATLAB simulation results show that very sophisticated dynamical behaviors and unique chaotic behaviors of the system. Finally, the definition and criterion of multi-scroll attractors for the translation-3 chaotic system is obtained. Three representative examples are shown in some classical chaotic systems that can be equally obtained via the set parameters of the translation type chaotic system. Furthermore, we show that the translation type chaotic systems have similar but topologically non-equivalent chaotic attractors, and they are the three-dimensional ordinary differential equations.
Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series
Directory of Open Access Journals (Sweden)
Qing Li
2016-01-01
Full Text Available According to the chaotic features and typical fractional order characteristics of the bearing vibration intensity time series, a forecasting approach based on long range dependence (LRD is proposed. In order to reveal the internal chaotic properties, vibration intensity time series are reconstructed based on chaos theory in phase-space, the delay time is computed with C-C method and the optimal embedding dimension and saturated correlation dimension are calculated via the Grassberger–Procaccia (G-P method, respectively, so that the chaotic characteristics of vibration intensity time series can be jointly determined by the largest Lyapunov exponent and phase plane trajectory of vibration intensity time series, meanwhile, the largest Lyapunov exponent is calculated by the Wolf method and phase plane trajectory is illustrated using Duffing-Holmes Oscillator (DHO. The Hurst exponent and long range dependence prediction method are proposed to verify the typical fractional order features and improve the prediction accuracy of bearing vibration intensity time series, respectively. Experience shows that the vibration intensity time series have chaotic properties and the LRD prediction method is better than the other prediction methods (largest Lyapunov, auto regressive moving average (ARMA and BP neural network (BPNN model in prediction accuracy and prediction performance, which provides a new approach for running tendency predictions for rotating machinery and provide some guidance value to the engineering practice.
An improved permutation-diffusion type image cipher with a chaotic orbit perturbing mechanism.
Chen, Jun-xin; Zhu, Zhi-liang; Fu, Chong; Yu, Hai
2013-11-18
During the past decades, chaos-based permutation-diffusion type image cipher has been widely investigated to meet the increasing demand for real-time secure image transmission over public networks. However, the existing researches almost exclusively focus on the improvements of the permutation and diffusion methods independently, without consideration of cooperation between the two processes. In this paper, an improved permutation-diffusion type image cipher with a chaotic orbit perturbing mechanism is proposed. In the permutation stage, pixels in the plain image are shuffled with a pixel-swapping mechanism, and the pseudorandom locations are generated by chaotic logistic map iteration. Furthermore, a plain pixel related chaotic orbit perturbing mechanism is introduced. As a result, a tiny change in plain image will be spread out during the confusion process, and hence an effective diffusion effect is introduced. By using a reverse direction diffusion method, the introduced diffusion effect will be further diffused to the whole cipher image within one overall encryption round. Simulation results and extensive cryptanalysis justify that the proposed scheme has a satisfactory security with a low computational complexity, which renders it a good candidate for real-time secure image storage and distribution applications.
Chaotic advection induced heat transfer enhancement in a chevron-type plate heat exchanger
Tohidi, A.; Hosseinalipour, S. M.; Taheri, P.; Nouri, N. M.; Mujumdar, A. S.
2013-11-01
The present work examines the role of chaotic mixing as a means of heat transfer enhancement in plate heat exchangers. In order to demonstrate the chaotic behavior, sensitivity to initial conditions and horseshoe maps are visualized. The Nusselt number and the friction factor were computed in the range of reynolds number, 1 < Re < 10. The Nusselt number increases considerably in chaotic models whereas the friction factor increases only marginally.
Experimental Study on Chaotic Mixing Created by a New Type of Mixer with Rotational Blades
Directory of Open Access Journals (Sweden)
Payam Rahim Mashaei
2012-01-01
Full Text Available The aim of this paper is an experimental investigation of laminar mixing in a new type of chaotic mixer, which has been proposed by Hwu (2008, by means of material line deformation. The mixer is a circular cavity with two rotational blades which move along a semicircular path and drive the fluid motion. The flow visualization is carried out by marking of the free surface of the flow with a tracer in working fluid. In the present study the effects of length and rotational speed of blades on mixing efficiency are evaluated by measuring of the area covered by the tracer. As a result, it is demonstrated that the goodness of mixing increases as rotational speed of blades increases. Also, it is detected that the mixing efficiency strongly depends on the lengths of rotating blades.
Ashrafi, S.; Roszman, L.
1991-01-01
Presented here is a preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. The authors show that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.
Waalkens, H.; Burbanks, A.; Wiggins, S.
2004-01-01
A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows us to compute
Energy Technology Data Exchange (ETDEWEB)
Kengne, Jacques [Laboratoire d' Automatique et Informatique Apliquée (LAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Bandjoun (Cameroon); Kenmogne, Fabien [Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototype, University of Yaoundé 1, Yaoundé (Cameroon)
2014-12-15
The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by using time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.
Cascade Chaotic System With Applications.
Zhou, Yicong; Hua, Zhongyun; Pun, Chi-Man; Chen, C L Philip
2015-09-01
Chaotic maps are widely used in different applications. Motivated by the cascade structure in electronic circuits, this paper introduces a general chaotic framework called the cascade chaotic system (CCS). Using two 1-D chaotic maps as seed maps, CCS is able to generate a huge number of new chaotic maps. Examples and evaluations show the CCS's robustness. Compared with corresponding seed maps, newly generated chaotic maps are more unpredictable and have better chaotic performance, more parameters, and complex chaotic properties. To investigate applications of CCS, we introduce a pseudo-random number generator (PRNG) and a data encryption system using a chaotic map generated by CCS. Simulation and analysis demonstrate that the proposed PRNG has high quality of randomness and that the data encryption system is able to protect different types of data with a high-security level.
Chaotic signal processing: information aspects
Andreyev, Y V; Efremova, E V; Anagnostopoulos, A N
2003-01-01
One of the features of chaotic signals that make them different of other types of signals is their special information properties. In this paper, we investigate the effect of these properties on the procedures of chaotic signal processing. On examples of cleaning chaotic signals off noise, chaotic synchronization and separation of chaotic signals we demonstrate the existence of basic limits imposed by information theory on chaotic signal processing, independent of concrete algorithms. Relations of these limits with the Second law, Shannon theorems and Landauer principle are discussed.
Kitazoe, Katsuma; Park, Yeon-Su; Kaji, Noritada; Okamoto, Yukihiro; Tokeshi, Manabu; Kogure, Kentaro; Harashima, Hideyoshi; Baba, Yoshinobu
2012-01-01
Multifunctional envelope-type nanodevices (MENDs) are very promising non-viral gene delivery vectors because they are biocompatible and enable programmed packaging of various functional elements into an individual nanostructured liposome. Conventionally MENDs have been fabricated by complicated, labor-intensive, time-consuming bulk batch methods. To avoid these problems in MEND fabrication, we adopted a microfluidic chip with a chaotic mixer array on the floor of its reaction channel. The array was composed of 69 cycles of the staggered chaotic mixer with bas-relief structures. Although the reaction channel had very large Péclet numbers (>10(5)) favorable for laminar flows, its chaotic mixer array led to very small mixing lengths (<1.5 cm) and that allowed homogeneous mixing of MEND precursors in a short time. Using the microfluidic chip, we fabricated a double-lamellar MEND (D-MEND) composed of a condensed plasmid DNA core and a lipid bilayer membrane envelope as well as the D-MEND modified with trans-membrane peptide octaarginine. Our lab-on-a-chip approach was much simpler, faster, and more convenient for fabricating the MENDs, as compared with the conventional bulk batch approaches. Further, the physical properties of the on-chip-fabricated MENDs were comparable to or better than those of the bulk batch-fabricated MENDs. Our fabrication strategy using microfluidic chips with short mixing length reaction channels may provide practical ways for constructing more elegant liposome-based non-viral vectors that can effectively penetrate all membranes in cells and lead to high gene transfection efficiency.
Directory of Open Access Journals (Sweden)
Katsuma Kitazoe
Full Text Available Multifunctional envelope-type nanodevices (MENDs are very promising non-viral gene delivery vectors because they are biocompatible and enable programmed packaging of various functional elements into an individual nanostructured liposome. Conventionally MENDs have been fabricated by complicated, labor-intensive, time-consuming bulk batch methods. To avoid these problems in MEND fabrication, we adopted a microfluidic chip with a chaotic mixer array on the floor of its reaction channel. The array was composed of 69 cycles of the staggered chaotic mixer with bas-relief structures. Although the reaction channel had very large Péclet numbers (>10(5 favorable for laminar flows, its chaotic mixer array led to very small mixing lengths (<1.5 cm and that allowed homogeneous mixing of MEND precursors in a short time. Using the microfluidic chip, we fabricated a double-lamellar MEND (D-MEND composed of a condensed plasmid DNA core and a lipid bilayer membrane envelope as well as the D-MEND modified with trans-membrane peptide octaarginine. Our lab-on-a-chip approach was much simpler, faster, and more convenient for fabricating the MENDs, as compared with the conventional bulk batch approaches. Further, the physical properties of the on-chip-fabricated MENDs were comparable to or better than those of the bulk batch-fabricated MENDs. Our fabrication strategy using microfluidic chips with short mixing length reaction channels may provide practical ways for constructing more elegant liposome-based non-viral vectors that can effectively penetrate all membranes in cells and lead to high gene transfection efficiency.
Mohammadzadeh, Ardashir; Ghaemi, Sehraneh
2015-09-01
This paper proposes a novel approach for training of proposed recurrent hierarchical interval type-2 fuzzy neural networks (RHT2FNN) based on the square-root cubature Kalman filters (SCKF). The SCKF algorithm is used to adjust the premise part of the type-2 FNN and the weights of defuzzification and the feedback weights. The recurrence property in the proposed network is the output feeding of each membership function to itself. The proposed RHT2FNN is employed in the sliding mode control scheme for the synchronization of chaotic systems. Unknown functions in the sliding mode control approach are estimated by RHT2FNN. Another application of the proposed RHT2FNN is the identification of dynamic nonlinear systems. The effectiveness of the proposed network and its learning algorithm is verified by several simulation examples. Furthermore, the universal approximation of RHT2FNNs is also shown.
Institute of Scientific and Technical Information of China (English)
FENG Cun-Fang; WANG Ying-Hai
2011-01-01
We study different types of projective synchronization (projective-anticipating, projective, and projectivelag synchronization) in a class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices.We relax some limitations of previous work, where the scaling factor a can not be any desired value.In this paper, we achieve projective-anticipating, projective, and projective-lag synchronization without the limitation of α.A suitable controller is chosen using active control approach.Based on the Lyapunov stability theory, we derive the sutficient stability condition through theoretical analysis.The analytical results are validated by the numerical simulations using Ikeda model and Mackey-Glass model.
Gitterman, Moshe
2010-01-01
Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom. This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multip
The study of fuzzy chaotic neural network based on chaotic method
Institute of Scientific and Technical Information of China (English)
WANG Ke-jun; TANG Mo; ZHANG Yan
2006-01-01
This paper proposes a type of Fuzzy Chaotic Neural Network (FCNN). Firstly, the model of recurrent fuzzy neural network (RFNN) is considered, which adds a feedback in the second layer to realize dynamic map. Then, the Logistic map is introduced into the recurrent fuzzy neural network, so as to build a Fuzzy Chaotic Neural Network (FCNN). Its chaotic character is analyzed, and then the training algorithm and associate memory ability are studied subsequently. And then, a chaotic system is approximated using FCNN; the simulation results indicate that FCNN could approach dynamic system preferably. And owing to the introducing of chaotic map, the chaotic recollect capacity of FCNN is increased.
PITCH ANGLE RESTRICTIONS IN LATE-TYPE SPIRAL GALAXIES BASED ON CHAOTIC AND ORDERED ORBITAL BEHAVIOR
Energy Technology Data Exchange (ETDEWEB)
Perez-Villegas, A.; Pichardo, B.; Moreno, E.; Peimbert, A. [Instituto de Astronomia, Universidad Nacional Autonoma de Mexico, A.P. 70-264, 04510 Mexico D.F. (Mexico); Velazquez, H. M., E-mail: barbara@astroscu.unam.mx [Observatorio Astronomico Nacional, Universidad Nacional Autonoma de Mexico, Apdo. Postal 877, 22800 Ensenada (Mexico)
2012-01-20
We built models for low bulge mass spiral galaxies (late type as defined by the Hubble classification) using a three-dimensional self-gravitating model for spiral arms, and analyzed the orbital dynamics as a function of pitch angle, ranging from 10 Degree-Sign to 60 Degree-Sign . Indirectly testing orbital self-consistency, we search for the main periodic orbits and studied the density response. For pitch angles up to approximately {approx}20 Degree-Sign , the response closely supports the potential readily permitting the presence of long-lasting spiral structures. The density response tends to 'avoid' larger pitch angles in the potential by keeping smaller pitch angles in the corresponding response. Spiral arms with pitch angles larger than {approx}20 Degree-Sign would not be long-lasting structures but would rather be transient. On the other hand, from an extensive orbital study in phase space, we also find that for late-type galaxies with pitch angles larger than {approx}50 Degree-Sign , chaos becomes pervasive, destroying the ordered phase space surrounding the main stable periodic orbits and even destroying them. This result is in good agreement with observations of late-type galaxies, where the maximum observed pitch angle is {approx}50 Degree-Sign .
Altmann, Eduardo G; Tél, Tamás
2015-01-01
We investigate chaotic dynamical systems for which the intensity of trajectories might grow unlimited in time. We show that (i) the intensity grows exponentially in time and is distributed spatially according to a fractal measure with an information dimension smaller than that of the phase space,(ii) such exploding cases can be described by an operator formalism similar to the one applied to chaotic systems with absorption (decaying intensities), but (iii) the invariant quantities characterizing explosion and absorption are typically not directly related to each other, e.g., the decay rate and fractal dimensions of absorbing maps typically differ from the ones computed in the corresponding inverse (exploding) maps. We illustrate our general results through numerical simulation in the cardioid billiard mimicking a lasing optical cavity, and through analytical calculations in the baker map.
Pitch Angle Restrictions in Late Type Spiral Galaxies Based on Chaotic and Ordered Orbital Behavior
Perez-Villegas, Angeles; Moreno, Edmundo; Peimbert, Antonio; Velazquez, Hector M
2011-01-01
We built models for low bulge mass spiral galaxies (late type as defined by the Hubble classification) using a 3-D self-gravitating model for spiral arms, and analyzed the orbital dynamics as a function of pitch angle, going from 10$\\deg$ to 60$\\deg$. Testing undirectly orbital self-consistency, we search for the main periodic orbits and studied the density response. For pitch angles up to approximately $\\sim 20\\deg$, the response supports closely the potential permitting readily the presence of long lasting spiral structures. The density response tends to "avoid" larger pitch angles in the potential, by keeping smaller pitch angles in the corresponding response. Spiral arms with pitch angles larger than $\\sim 20\\deg$, would not be long-lasting structures but rather transient. On the other hand, from an extensive orbital study in phase space, we also find that for late type galaxies with pitch angles larger than $\\sim 50\\deg$, chaos becomes pervasive destroying the ordered phase space surrounding the main sta...
2003-01-01
[figure removed for brevity, see original site] Released 4 June 2003Chaotic terrain on Mars is thought to form when there is a sudden removal of subsurface water or ice, causing the surface material to slump and break into blocks. The chaotic terrain in this THEMIS visible image is confined to a crater just south of Elysium Planitia. It is common to see chaotic terrain in the vicinity of the catastrophic outflow channels on Mars, but the terrain in this image is on the opposite side of the planet from these channels, making it somewhat of an oddity.Image information: VIS instrument. Latitude -5.9, Longitude 108.1 East (251.9 West). 19 meter/pixel resolution.Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
The transient ladder synchronization of chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Chen, H.-K. [Department of Industrial Engineering and Management, Hsiuping Institute of Technology, No. 11, Gungye Rd., Dali City, Taichung, Taiwan (China)]. E-mail: kanechen@giga.net.tw; Sheu, L.-J. [Department of Mechanical Engineering, Chung Hua University, Hsinchu, Taiwan (China)]. E-mail: ljsheu@chu.edu.tw
2006-07-03
A new type for chaotically synchronizing systems, transient ladder chaos synchronization, is proposed in this Letter. For some physical systems, chaotic synchronization is possible in only some of the variables. It is shown that, for the non-synchronizing variable, synchronization up to a constant difference for t{sub 1}=
Characterizing chaotic melodies in automatic music composition.
Coca, Andrés E; Tost, Gerard O; Zhao, Liang
2010-09-01
In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.
Characterizing chaotic melodies in automatic music composition
Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang
2010-09-01
In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.
The transition to chaotic phase synchronization
DEFF Research Database (Denmark)
Mosekilde, E.; Laugesen, J. L.; Zhusubaliyev, Zh. T.
2012-01-01
The transition to chaotic phase synchronization for a periodically driven spiral-type chaotic oscillator is known to involve a dense set of saddle-node bifurcations. By following the synchronization transition through the cascade of period-doubling bifurcations in a forced Ro¨ssler system, this p...
Chaotic Dynamics in Hybrid Systems
P.J. Collins (Pieter)
2008-01-01
htmlabstractIn this paper we give an overview of some aspects of chaotic dynamics in hybrid systems, which comprise different types of behaviour. Hybrid systems may exhibit discontinuous dependence on initial conditions leading to new dynamical phenomena. We indicate how methods from topological
Chaotic dynamics in hybrid systems
P.J. Collins (Pieter)
2008-01-01
htmlabstractIn this paper we give an overview of some aspects of chaotic dynamics in hybrid systems, which comprise different types of behaviour. Hybrid systems may exhibit discontinuous dependence on initial conditions leading to new dynamical phenomena. We indicate how methods from topological
Chaotic communication scheme with multiplication
Bobreshov, A. M.; Karavaev, A. A.
2007-05-01
A new scheme of data transmission with nonlinear admixing is described, in which the two mutually inverse operations (multiplication and division) ensure multiplicative mixing of the informative and chaotic signals that provides a potentially higher degree of security. A special feature of the proposed scheme is the absence of limitations (related to the division by zero) imposed on the types of informative signals.
Approximating chaotic saddles for delay differential equations
Taylor, S. Richard; Campbell, Sue Ann
2007-04-01
Chaotic saddles are unstable invariant sets in the phase space of dynamical systems that exhibit transient chaos. They play a key role in mediating transport processes involving scattering and chaotic transients. Here we present evidence (long chaotic transients and fractal basins of attraction) of transient chaos in a “logistic” delay differential equation. We adapt an existing method (stagger-and-step) to numerically construct the chaotic saddle for this system. This is the first such analysis of transient chaos in an infinite-dimensional dynamical system, and in delay differential equations in particular. Using Poincaré section techniques we illustrate approaches to visualizing the saddle set, and confirm that the saddle has the Cantor-like fractal structure consistent with a chaotic saddle generated by horseshoe-type dynamics.
Institute of Scientific and Technical Information of China (English)
ShiEnhui; ZhouLizhen; ZhouYoucheng
2003-01-01
It is proved that there is no chaotic group actions on any topological space with free arc.In this paper the chaotic actions of the group like G×F,where F is a finite group,are studied.In particular,under a suitable assumption ,if F is a cyclic group,then the topological space which admits a chaotic action of Z×F must admit a chatotic homeomorphism.A topological space which admits a chaotic group action but admits no chaotic horneomorphism is constructed.
Deciphering Secure Chaotic Communication
Mathiazhagen, C
1999-01-01
A simple technique for decoding an unknown modulated chaotic time-series is presented. We point out that, by fitting a polynomial model to the modulated chaotic signal, the error in the fit gives sufficient information to decode the modulating signal. For analog implementation, a lowpass filter can be used for fitting. This method is simple and easy to implement in hardware.
Chaotic dynamics of controlled electric power systems
Kozlov, V. N.; Trosko, I. U.
2016-12-01
The conditions for appearance of chaotic dynamics of electromagnetic and electromechanical processes in energy systems described by the Park-Gorev bilinear differential equations with account for lags of coordinates and restrictions on control have been formulated. On the basis of classical equations, the parameters of synchronous generators and power lines, at which the chaotic dynamics of energy systems appears, have been found. The qualitative and quantitative characteristics of chaotic processes in energy associations of two types, based on the Hopf theorem, and methods of nonstationary linearization and decompositions are given. The properties of spectral characteristics of chaotic processes have been investigated, and the qualitative similarity of bilinear equations of power systems and Lorentz equations have been found. These results can be used for modernization of the systems of control of energy objects. The qualitative and quantitative characteristics for power energy systems as objects of control and for some laws of control with the feedback have been established.
Synchronization of chaotic systems.
Pecora, Louis M; Carroll, Thomas L
2015-09-01
We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.
Rising Above Chaotic Likelihoods
Du, Hailiang
2014-01-01
Berliner (Likelihood and Bayesian prediction for chaotic systems, J. Am. Stat. Assoc. 1991) identified a number of difficulties in using the likelihood function within the Bayesian paradigm for state estimation and parameter estimation of chaotic systems. Even when the equations of the system are given, he demonstrated "chaotic likelihood functions" of initial conditions and parameter values in the 1-D Logistic Map. Chaotic likelihood functions, while ultimately smooth, have such complicated small scale structure as to cast doubt on the possibility of identifying high likelihood estimates in practice. In this paper, the challenge of chaotic likelihoods is overcome by embedding the observations in a higher dimensional sequence-space, which is shown to allow good state estimation with finite computational power. An Importance Sampling approach is introduced, where Pseudo-orbit Data Assimilation is employed in the sequence-space in order first to identify relevant pseudo-orbits and then relevant trajectories. Es...
Synchronization of chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Pecora, Louis M.; Carroll, Thomas L. [U.S. Naval Research Laboratory, Washington, District of Columbia 20375 (United States)
2015-09-15
We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.
Suzuki, Hideyuki; Imura, Jun-ichi; Horio, Yoshihiko; Aihara, Kazuyuki
2013-01-01
The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented.
Simple Autonomous Chaotic Circuits
Piper, Jessica; Sprott, J.
2010-03-01
Over the last several decades, numerous electronic circuits exhibiting chaos have been proposed. Non-autonomous circuits with as few as two components have been developed. However, the operation of such circuits relies on the non-ideal behavior of the devices used, and therefore the circuit equations can be quite complex. In this paper, we present two simple autonomous chaotic circuits using only opamps and linear passive components. The circuits each use one opamp as a comparator, to provide a signum nonlinearity. The chaotic behavior is robust, and independent of nonlinearities in the passive components. Moreover, the circuit equations are among the algebraically simplest chaotic systems yet constructed.
New developments in classical chaotic scattering.
Seoane, Jesús M; Sanjuán, Miguel A F
2013-01-01
Classical chaotic scattering is a topic of fundamental interest in nonlinear physics due to the numerous existing applications in fields such as celestial mechanics, atomic and nuclear physics and fluid mechanics, among others. Many new advances in chaotic scattering have been achieved in the last few decades. This work provides a current overview of the field, where our attention has been mainly focused on the most important contributions related to the theoretical framework of chaotic scattering, the fractal dimension, the basins boundaries and new applications, among others. Numerical techniques and algorithms, as well as analytical tools used for its analysis, are also included. We also show some of the experimental setups that have been implemented to study diverse manifestations of chaotic scattering. Furthermore, new theoretical aspects such as the study of this phenomenon in time-dependent systems, different transitions and bifurcations to chaotic scattering and a classification of boundaries in different types according to symbolic dynamics are also shown. Finally, some recent progress on chaotic scattering in higher dimensions is also described.
Fractional order control and synchronization of chaotic systems
Vaidyanathan, Sundarapandian; Ouannas, Adel
2017-01-01
The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos synchronization, jerk circuits, fractional chaotic systems with hidden attractors, neural network, fuzzy logic controllers, behavioral modeling, robust and adaptive control, sliding mode control, different types of synchronization, circuit realization of chaotic systems, etc. In addition to providing readers extensive information on chaos fundamentals, fractional calculus, fractional differential equations, fractional contro...
Directory of Open Access Journals (Sweden)
Rodrigo Méndez-Ramírez
2017-01-01
Full Text Available This paper presents a new three-dimensional autonomous chaotic system. The proposed system generates a chaotic attractor with the variation of two parameters. Analytical and numerical studies of the dynamic properties to generate chaos, for continuous version (CV and discretized version (DV, for the new chaotic system (NCS were conducted. The CV of the NCS was implemented by using an electronic circuit with operational amplifiers (OAs. In addition, the presence of chaos for DV of the NCS was proved by using the analytical and numerical degradation tests; the time series was calculated to determine the behavior of Lyapunov exponents (LEs. Finally, the DV of NCS was implemented, in real-time, by using a novel embedded system (ES Mikromedia Plus for PIC32MX7 that includes one microcontroller PIC32 and one thin film transistor touch-screen display (TFTTSD, together with external digital-to-analog converters (DACs.
Senkerik, Roman; Zelinka, Ivan; Pluhacek, Michal; Davendra, Donald; Oplatková Kominkova, Zuzana
2014-01-01
Evolutionary technique differential evolution (DE) is used for the evolutionary tuning of controller parameters for the stabilization of set of different chaotic systems. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used also as the chaotic pseudorandom number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudorandom sequences given by chaotic map to help differential evolution algorithm search for the best controller settings for the very same chaotic system. The optimizations were performed for three different chaotic systems, two types of case studies and developed cost functions.
Directory of Open Access Journals (Sweden)
Roman Senkerik
2014-01-01
Full Text Available Evolutionary technique differential evolution (DE is used for the evolutionary tuning of controller parameters for the stabilization of set of different chaotic systems. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used also as the chaotic pseudorandom number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudorandom sequences given by chaotic map to help differential evolution algorithm search for the best controller settings for the very same chaotic system. The optimizations were performed for three different chaotic systems, two types of case studies and developed cost functions.
Regular and Chaotic Regimes in Scalar Field Cosmology
Directory of Open Access Journals (Sweden)
Alexey V. Toporensky
2006-03-01
Full Text Available A transient chaos in a closed FRW cosmological model with a scalar field is studied. We describe two different chaotic regimes and show that the type of chaos in this model depends on the scalar field potential. We have found also that for sufficiently steep potentials or for potentials with large cosmological constant the chaotic behavior disappears.
Enhancing chaoticity of spatiotemporal chaos.
Li, Xiaowen; Zhang, Heqiao; Xue, Yu; Hu, Gang
2005-01-01
In some practical situations strong chaos is needed. This introduces the task of chaos control with enhancing chaoticity rather than suppressing chaoticity. In this paper a simple method of linear amplifications incorporating modulo operations is suggested to make spatiotemporal systems, which may be originally chaotic or nonchaotic, strongly chaotic. Specifically, this control can eliminate periodic windows, increase the values and the number of positive Lyapunov exponents, make the probability distributions of the output chaotic sequences more homogeneous, and reduce the correlations of chaotic outputs for different times and different space units. The applicability of the method to practical tasks, in particular to random number generators and secure communications, is briefly discussed.
Chaotic LIDAR for Naval Applications
2014-09-30
LIDAR for Naval Applications: FY12 Progress Report (7/1/2014- 9/30/2014) This document provides a progress report on the project "Chaotic LIDAR for...digital receiver to form a chaotic LIDAR (CLIDAR) ranging system. The design of the chaotic fiber ring laser and the fiber amplifiers are guided by...Wideband Amplifier Chain High Power Blue-Green Ranging Fig 1. The chaotic LIDAR (CLIDAR) transmitter approach. Several stages are used to
Digital image encryption with chaotic map lattices
Institute of Scientific and Technical Information of China (English)
Sun Fu-Yan; Lü Zong-Wang
2011-01-01
This paper proposes a secure approach for encryption and decryption of digital images with chaotic map lattices.In the proposed encryption process, eight different types of operations are used to encrypt the pixels of an image and one of them will be used for particular pixels decided by the outcome of the chaotic map lattices. To make the cipher more robust against any attacks, the secret key is modified after encrypting each block of sixteen pixels of the image.The experimental results and security analysis show that the proposed image encryption scheme achieves high security and efficiency.
Chaotic Turing pattern formation in spatiotemporal systems
Institute of Scientific and Technical Information of China (English)
XIAO Jing-hua; LI Hai-hong; YANG Jun-zhong; HU Gang
2006-01-01
The problem of Turing pattern formation has attracted much attention in nonlinear science as well as physics,chemistry and biology.So far spatially ordered Turing patterns have been observed in stationary and oscillatory media only.In this paper we find that spatially ordered Turing patterns exist in chaotic extended systems.And chaotic Turing patterns are strikingly rich and surprisingly beautiful with their space structures.These findings are in sharp contrast with the intuition of pseudo-randomness of chaos.The richness and beauty of the chaotic Turing patterns are attributed to a large variety of symmetry properties realized by various types of self-organizations of partial chaos synchronizations.
IMPULSIVE CONTROL OF CHAOTIC ATTRACTORS IN NONLINEAR CHAOTIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
马军海; 任彪; 陈予恕
2004-01-01
Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented.By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such kind of nonlinear chaotic system has been deduced, and with it, the upper bond of the impulse interval for asymptotically stable control was given. Numerical results are presented, which are considered with important reference value for control of chaotic attractors.
Synchronization of chaotic VCSELs by external chaotic signal parameter modulation
Institute of Scientific and Technical Information of China (English)
Wei Wang; Shenghai Zhang; Xingzhong Qian; Yanbin Wang
2009-01-01
Synchronization of chaotic vertical-cavity surface-emitting lasers (VCSELs) is achieved by external chaotic signal modulation successfully.Simulation indicates that we can get chaos synchronization if the intensity of external chaotic signal is large enough.First of all,we use direct current modulation to achieve the chaos of VCSELs,and determine the laser's chaotic state by analyzing time series of the output and the corresponding power spectrum.And then we achieve synchronization of the two chaotic systems by external chaotic signal parameter modulation.We also find that the larger the modulation intensity is,the easier it is to achieve synchronization for chaotic VCSELs.This approach can also be applied to systems with a number of modulated lasers.
Inhomogeneous stationary and oscillatory regimes in coupled chaotic oscillators.
Liu, Weiqing; Volkov, Evgeny; Xiao, Jinghua; Zou, Wei; Zhan, Meng; Yang, Junzhong
2012-09-01
The dynamics of linearly coupled identical Lorenz and Pikovsky-Rabinovich oscillators are explored numerically and theoretically. We concentrate on the study of inhomogeneous stable steady states ("oscillation death (OD)" phenomenon) and accompanying periodic and chaotic regimes that emerge at an appropriate choice of the coupling matrix. The parameters, for which OD occurs, are determined by stability analysis of the chosen steady state. Three model-specific types of transitions to and from OD are observed: (1) a sharp transition to OD from a nonsymmetric chaotic attractor containing random intervals of synchronous chaos; (2) transition to OD from the symmetry-breaking chaotic regime created by negative coupling; (3) supercritical bifurcation of OD into inhomogeneous limit cycles and further evolution of the system to inhomogeneous chaotic regimes that coexist with complete synchronous chaos. These results may fill a gap in the understanding of the mechanism of OD in coupled chaotic systems.
Chandramouli, V. V. M. S.; Martens, M.; De Melo, W.; Tresser, C. P.
2009-01-01
The period doubling renormalization operator was introduced by Feigenbaum and by Coullet and Tresser in the 1970s to study the asymptotic small-scale geometry of the attractor of one-dimensional systems that are at the transition from simple to chaotic dynamics. This geometry turns out not to depend
Security analysis and modification of a chaotic encryption system
Institute of Scientific and Technical Information of China (English)
崔光亮; 冯正进; 胡国杰
2004-01-01
A type of digital chaotic encryption system was proposed in Ref. [1] which uses a class of 1-D piecewise linear (PWL) map to realize chaotic encryption and decryption system through the inverse system approach. In the general with the input terminal. In this paper we show that this cryptosystem can not frustrate chosen-cipher text attack. A type of chaotic encryption system based on self-synchronizing stream cipher is proposed. This system can avoid chosen-cipher text attack and has higher security.
Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators
Hramov, Alexander E.; ALEXEY A. KORONOVSKII
2005-01-01
A new behavior type of unidirectionally coupled chaotic oscillators near the generalized synchronization transition has been detected. It has been shown that the generalized synchronization appearance is preceded by the intermitted behavior: close to threshold parameter value the coupled chaotic systems demonstrate the generalized synchronization most of the time, but there are time intervals during which the synchronized oscillations are interrupted by non-synchronous bursts. This type of th...
Periodicity of chaotic solutions
Berezowski, Marek
2016-01-01
The scope of the paper is the analysis of the impact of flow reversal on the dynamics of cascades of reactors. Periodic and chaotic oscillations occur in the analyzed system. There is a dependence between the oscillation period of the state variable of the system without flow reversal and the recurrence period of windows of chaos in the steady-state diagram of the system with flow reversal.
Frontiers of chaotic advection
Aref, Hassan; Budišić, Marko; Cartwright, Julyan H E; Clercx, Herman J H; Feudel, Ulrike; Golestanian, Ramin; Gouillart, Emmanuelle; Guer, Yves Le; van Heijst, GertJan F; Krasnopolskaya, Tatyana S; MacKay, Robert S; Meleshko, Vyacheslav V; Metcalfe, Guy; Mezić, Igor; de Moura, Alessandro P S; Omari, Kamal El; Piro, Oreste; Speetjens, Michel F M; Sturman, Rob; Thiffeault, Jean-Luc; Tuval, Idan
2014-01-01
We review the present position of and survey future perspectives in the physics of chaotic advection; the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, micro-fluidics, biological flows, and large-scale dispersion of pollutants in oceanographic and atmospheric flows.
Charged Particle Motion in Temporal Chaotic and Spatiotemporal Chaotic Fields
Institute of Scientific and Technical Information of China (English)
张海云; 贺凯芬
2002-01-01
We investigate charged particle motion in temporal chaotic and spatiotemporal chaotic fields. In its steady wave frame a few key modes of the solution of the driven/damped nonlinear wave equation are used as the field. It is found that in the spatiotemporal chaotic field the particle drifts relative to the steady wave, in contrast to that in the temporal chaotic field where the particle motion is localized in a trough of the wave field. The result is of significance for understanding stochastic acceleration of particles.
Pattern formations in chaotic spatio-temporal systems
Indian Academy of Sciences (India)
Ying Zhang; Shihong Wang; Jinhua Xiao; Hilda A Cerdeira; S Chen; Gang Hu
2005-06-01
Pattern formations in chaotic spatio-temporal systems modelled by coupled chaotic oscillators are investigated. We focus on various symmetry breakings and different kinds of chaos synchronization–desynchronization transitions, which lead to certain types of spontaneous spatial orderings and the emergence of some typical ordered patterns, such as rotating wave patterns with splay phase ordering (orientational symmetry breaking) and partially synchronous standing wave patterns with in-phase ordering (translational symmetry breaking). General pictures of the global behaviors of pattern formations and transitions in coupled chaotic oscillators are provided.
Cryptography with chaotic mixing
Energy Technology Data Exchange (ETDEWEB)
Oliveira, Luiz P.L. de [Programa Interdisciplinar de Pos-Graduacao em Computacao Aplicada - PIPCA, Universidade do Vale do Rio dos Sinos - UNISINOS, Av. Unisinos 950, 93022-000 Sao Leopoldo, RS (Brazil)], E-mail: lpluna@unisinos.br; Sobottka, Marcelo [Centro de Modelamiento Matematico, Universidad de Chile, Blanco Encalada 2120, 7o piso Casilla 170/3, Correo 3, Santiago (Chile)], E-mail: sobottka@dim.uchile.cl
2008-02-15
We propose a cryptosystem based on one-dimensional chaotic maps of the form H{sub p}(x)=r{sub p}{sup -1}0G0r{sub p}(x) defined in the interval [0, 10{sup p}) for a positive integer parameter p, where G(x)=10x(mod10) and r{sub p}(x)={sup p}{radical}(x), which is a topological conjugacy between G and the shift map {sigma} on the space {sigma} of the sequences with 10 symbols. There are three advantages in comparison with the recently proposed cryptosystem based on chaotic logistic maps F{sub {mu}}(x)={mu}x(1-x) with 3 < {mu} {<=} 4: (a) H{sub p} is always chaotic for all parameters p, (b) the knowledge of an ergodic measure allows assignments of the alphabetic symbols to equiprobable sites of H{sub p}'s domain and (c) for each p, the security of the cryptosystem is manageable against brute force attacks.
Energy Technology Data Exchange (ETDEWEB)
Liu, Xiaojun [State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi' an Jiaotong University, Xi' an 710049 (China); School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001 (China); Hong, Ling, E-mail: hongling@mail.xjtu.edu.cn; Jiang, Jun [State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi' an Jiaotong University, Xi' an 710049 (China)
2016-08-15
Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuous change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.
Liu, Xiaojun; Hong, Ling; Jiang, Jun
2016-08-01
Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuous change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.
Liu, Xiaojun; Hong, Ling; Jiang, Jun
2016-08-01
Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuous change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.
Super Persistent Chaotic Transients And Catastrophic Bifurcation From Riddled To Fractal Basins
Andrade, V A
2002-01-01
This dissertation treats two related problems in chaotic dynamics: (1) super persistent chaotic transients in physical systems, and (2) catastrophic bifurcation from riddled to fractal basins. For the first problem, we investigate super persistent chaotic transient by studying the effect of noise on phase synchronization of coupled chaotic oscillators. A super persistent chaotic transient is typically induced by an unstable-unstable pair bifurcation in which two unstable periodic orbits of the same period coalesce and disappear as a system parameter is changed through a critical value. So far examples illustrating this type of transient chaos utilize discrete-time maps. We present a class of continuous-time dynamical systems that exhibit super persistent chaotic transients in parameter regimes of positive measure. In particular, we examine the effect of noise on phase synchronization of coupled chaotic oscillators. It is found that additive white noise can induce phase slips in integer multi...
Directory of Open Access Journals (Sweden)
Roman Senkerik
2016-01-01
Full Text Available In this paper, evolutionary technique Differential Evolution (DE is used for the evolutionary tuning of controller parameters for the stabilization of selected discrete chaotic system, which is the two-dimensional Lozi map. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used within Chaos enhanced heuristic concept as the chaotic pseudo-random number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudo-random sequences given by chaotic map to help Differential evolution algorithm in searching for the best controller settings for the same chaotic system. The optimizations were performed for three different required final behavior of the chaotic system, and two types of developed cost function. To confirm the robustness of presented approach, comparisons with canonical DE strategy and PSO algorithm have been performed.
Chaotic Control of Network Traffic
Institute of Scientific and Technical Information of China (English)
YANG Tan; CUI Yi-Dong; JIN Yue-Hui; CHENG Shi-Duan
2009-01-01
A method of chaotic control on network traffic is presented.By this method,the chaotic network traffic can be controlled to a pre-assigned equilibrium point according to chaotic prediction and the largest Lyapunov exponent of the traffic on congested link is reduced,thereby the probability of traffic burst and network congestion can be reduced.Numerical examples show that this method is effective.
Dynamic control of chaotic resonators
Di Falco, A.
2016-02-16
We report on the all-optical control of chaotic optical resonators based on silicon on insulator (SOI) platform. We show that simple non-chaotic cavities can be tuned to exhibit chaotic behavior via intense optical pump- ing, inducing a local change of refractive index. To this extent we have fabricated a number of devices and demonstrated experimentally and theoretically that chaos can be triggered on demand on an optical chip. © 2016 SPIE.
Touma, Jihad; Wisdom, Jack
1993-01-01
The discovery (by Laskar, 1989, 1990) that the evolution of the solar system is chaotic, made in a numerical integration of the averaged secular approximation of the equations of motions for the planets, was confirmed by Sussman and Wisdom (1992) by direct numerical integration of the whole solar system. This paper presents results of direct integrations of the rotation of Mars in the chaotically evolved planetary system, made using the same model as that used by Sussman and Wisdom. The numerical integration shows that the obliquity of Mars undergoes large chaotic variations, which occur as the system evolves in the chaotic zone associated with a secular spin-orbit resonance.
Advective Coalescence in Chaotic Flows
Energy Technology Data Exchange (ETDEWEB)
Nishikawa, Takashi; Toroczkai, Zoltan; Grebogi, Celso
2001-07-16
We investigate the reaction kinetics of small spherical particles with inertia, obeying coalescence type of reaction, B+B{yields}B , and being advected by hydrodynamical flows with time-periodic forcing. In contrast to passive tracers, the particle dynamics is governed by the strongly nonlinear Maxey-Riley equations, which typically create chaos in the spatial component of the particle dynamics, appearing as filamental structures in the distribution of the reactants. Defining a stochastic description supported on the natural measure of the attractor, we show that, in the limit of slow reaction, the reaction kinetics assumes a universal behavior exhibiting a t{sup -1} decay in the amount of reagents, which become distributed on a subset of dimension D{sub 2} , where D{sub 2} is the correlation dimension of the chaotic flow.
Chaotic and Chaos-Like Behavior in Continued Fractions
Shuji, OBATA; Shigeru, OHKURO; Toshiaki, MAEDA; Physics Laboratory, Faculty of Science and Engineering, Tokyo Denki University; Laboratory of Information aud System Engineering, Hachinohe Institute of Technology; DEPARTMENT OF MATHEMATICAL SCIENCES, TOKYO DENKI UNIVERSITY
1999-01-01
Chaotic and chaos-like behavior in continued fractions is studied with respect to several types of maps, including a logistic map. Various numerical phenomena in the continued fractions are investigated, where the fractions correspond to fractal structures. Cyclic terms in the Cauchy distribution areas are introduced, including the chaos-like behavior. It is indicated that such mixed states of distributions and cycles are common in the chaotic and chaos-like behavior.
Gills, Zelda; Roy, Rajarshi
1995-01-01
Irregular fluctuations in intensity have long plagued the operation of a wide variety of solid-state lasers. We are exploring the possibility of exploiting rather than avoiding a laser's chaotic output. As an important step in that direction, we have applied a novel control technique to stabilize a solid state laser. By making small periodic changes in only one input parameter of the laser, we are able to stabilize complex periodic waveforms and steady state behavior in the laser output. We demonstrate the application of this approach in a diode pumped Nd:/YAG laser system.
Binzel, R. P.; Green, J. R.; Opal, C. B.
1986-01-01
Thomas et al. (1984) analyzed 14 Voyager 2 images of Saturn's satellite Hyperion and interpreted them to be consistent with a coherent (nonchaotic) rotation period of 13.1 days. This interpretation was criticized by Peale and Wisdom (1984), who argued that the low sampling frequency of Voyager data does not allow chaotic or nonchaotic rotation to be distinguished. New observations obtained with a higher sampling frequency are reported here which conclusively show that the 13.1 day period found by Thomas et al. was not due to coherent rotation.
DEFF Research Database (Denmark)
Schäfer, Mirko; Greiner, Martin
Chaotic strings are coupled Tchebyscheff maps on a ring-network. With a well-specified empirical prescription they are able to explain the coupling constants of the standard model of elementary particle physics. This empirical relationship is tested further by introducing a tunable disorder to ch...... of the standard model of elementary particle physics. For the electromagnetic sector it is found that already a small disorder pushes the associated energy scale of the running coupling constant far away from the result without disorder....
Chaotic ray propagation in corrugated layers
Directory of Open Access Journals (Sweden)
M. Bottiglieri
2005-01-01
Full Text Available The aim of this paper is to study the effects of a corrugated wall on the behaviour of propagating rays. Different types of corrugation are considered, using different distributions of the corrugation heights: white Gaussian, power law, self-affine perturbation. In phase space, a prevalent chaotic behaviour of rays, and the presence of a lot of caustics, are observed. These results entail that the KAM theorem is not fulfilled.
Blowout bifurcation of chaotic saddles
Directory of Open Access Journals (Sweden)
Tomasz Kapitaniak
1999-01-01
Full Text Available Chaotic saddles are nonattracting dynamical invariant sets that can lead to a variety of physical phenomena. We describe the blowout bifurcation of chaotic saddles located in the symmetric invariant manifold of coupled systems and discuss dynamical phenomena associated with this bifurcation.
Chaotic systems in optical communications
Siuzdak, J.
2016-09-01
Communications application of chaotic oscillations of lasers with optoelectronic feedback was discussed. The possibility of eavesdropping of the transmission was analyzed. It was proved that if the rogue party precisely knows parameters of the chaotic system it may recreate the entire signals solely by observation of the optical signal power causing security breach.
Attractor switching by neural control of chaotic neurodynamics.
Pasemann, F; Stollenwerk, N
1998-11-01
Chaotic attractors of discrete-time neural networks include infinitely many unstable periodic orbits, which can be stabilized by small parameter changes in a feedback control. Here we explore the control of unstable periodic orbits in a chaotic neural network with only two neurons. Analytically, a local control algorithm is derived on the basis of least squares minimization of the future deviations between actual system states and the desired orbit. This delayed control allows a consistent neural implementation, i.e. the same types of neurons are used for chaotic and controlling modules. The control signal is realized with one layer of neurons, allowing selective switching between different stabilized periodic orbits. For chaotic modules with noise, random switching between different periodic orbits is observed.
Solving large scale traveling salesman problems by chaotic neurodynamics.
Hasegawa, Mikio; Ikeguch, Tohru; Aihara, Kazuyuki
2002-03-01
We propose a novel approach for solving large scale traveling salesman problems (TSPs) by chaotic dynamics. First, we realize the tabu search on a neural network, by utilizing the refractory effects as the tabu effects. Then, we extend it to a chaotic neural network version. We propose two types of chaotic searching methods, which are based on two different tabu searches. While the first one requires neurons of the order of n2 for an n-city TSP, the second one requires only n neurons. Moreover, an automatic parameter tuning method of our chaotic neural network is presented for easy application to various problems. Last, we show that our method with n neurons is applicable to large TSPs such as an 85,900-city problem and exhibits better performance than the conventional stochastic searches and the tabu searches.
The chaotic rotation of Hyperion
Wisdom, J.; Peale, S. J.; Mignard, F.
1984-01-01
Under the assumption that the satellite is rotating about a principal axis that is normal to its orbit plane, a plot of spin rate-versus-orientation for Hyperion at the pericenter of its orbit has revealed a large, chaotic zone surrounding Hyperion's synchronous spin-orbit state. The chaotic zone is so large that it surrounds the 1/2 and 2 states, and libration in the 3/2 state is not possible. Rotation in the chaotic zone is also attitude-unstable. As tidal dissipation drives Hyperion's spin toward a nearly synchronous value, Hyperion necessarily enters the large chaotic zone, becoming attitude-unstable and tumbling. It is therefore predicted that Hyperion will be found to be tumbling chaotically.
Amplitude envelope synchronization in coupled chaotic oscillators.
Gonzalez-Miranda, J M
2002-03-01
A peculiar type of synchronization has been found when two Van der Pol-Duffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and gradually larger in absolute value. This phenomenon is characterized by an appropriate correlation function between the returns of the signals, and interpreted in terms of the mutual excitation of new frequencies in the oscillators power spectra. This form of synchronization also occurs in other systems, but it shows up mixed with or screened by other forms of synchronization, as illustrated in this paper by means of the examples of the dynamic behavior observed for three other different models of chaotic oscillators.
ON FEEDBACK CONTROL OF DELAYED CHAOTIC SYSTEM
Institute of Scientific and Technical Information of China (English)
李丽香; 彭海朋; 卢辉斌; 关新平
2001-01-01
In this paper two different types of feedback control technique are discussed: the standard feedback control and the time-delay feedback control which have been successfully used in many control systems. In order to understand to what extent the two different types of control technique are useful in delayed chaotic systems, some analytic stabilization conditions for chaos control from the two types of control technique are derived based on Lyapunov stabilization arguments. Similarly, we discuss the tracking problem by applying the time-delay feedback control. Finally, numerical examples are provided.
A Novel Concatenated Chaotic Communication System
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A strategy for a novel concatenated chaotic communication system is presented. The transmitter system comprises chaotic turbo encoder and logistic CSK block in a serially concatenated form. Chaotic turbo code is capable of reducing bit error rate (BER) of the chaotic system in the AWGN channel. Through the chaotic turbo encoder, the coded sequence, which has quasi-chaotic properties, will be transmitted into the logistic CSK block. Having a very sensitive dependence on initial conditions of the map, the logistic CSK block can also be taken as the chaotic authentication method. The receiver, which has logistic demodulation block and chaotic decoder, is a linear asymptotic approximation to the inverse of the transmitter system. A chaotic iterative soft-decision decoding algorithm is also developed based on conventional maximum A posteriori decoding algorithm. At last, a two-step authentication method of this chaotic system is also presented.
Altmann, Eduardo G; Tél, Tamás
2013-01-01
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties of the closed system. In this paper we provide an unified treatment of leaking systems and we review applications to different physical problems, both in the classical and quantum pictures. Our treatment is based on the transient chaos theory of open systems, which is essential because real leaks have finite size and therefore estimations based on the closed system differ essentially from observations. The field of applications reviewed is very broad, ranging from planetary astronomy and hydrodynamical flows, to plasma physics and quantum fidelity. The theory is expanded and adapted to the case of partial leaks (partial absorption/transmission) with applications to room acoustics and optical microcavities in mind. Simulations in the lima .con family of billiards illustrate...
Chaotic systems with absorption
Altmann, Eduardo G; Tél, Tamás
2013-01-01
Motivated by applications in optics and acoustics we develop a dynamical-system approach to describe absorption in chaotic systems. We introduce an operator formalism from which we obtain (i) a general formula for the escape rate $\\kappa$ in terms of the natural conditionally-invariant measure of the system; (ii) an increased multifractality when compared to the spectrum of dimensions $D_q$ obtained without taking absorption and return times into account; and (iii) a generalization of the Kantz-Grassberger formula that expresses $D_1$ in terms of $\\kappa$, the positive Lyapunov exponent, the average return time, and a new quantity, the reflection rate. Simulations in the cardioid billiard confirm these results.
Chaotic advection in blood flow.
Schelin, A B; Károlyi, Gy; de Moura, A P S; Booth, N A; Grebogi, C
2009-07-01
In this paper we argue that the effects of irregular chaotic motion of particles transported by blood can play a major role in the development of serious circulatory diseases. Vessel wall irregularities modify the flow field, changing in a nontrivial way the transport and activation of biochemically active particles. We argue that blood particle transport is often chaotic in realistic physiological conditions. We also argue that this chaotic behavior of the flow has crucial consequences for the dynamics of important processes in the blood, such as the activation of platelets which are involved in the thrombus formation.
Modeling of Coupled Chaotic Oscillators
Energy Technology Data Exchange (ETDEWEB)
Lai, Y. [Departments of Physics and Astronomy and of Mathematics, University of Kansas, Lawrence, Kansas 66045 (United States); Grebogi, C. [Institute for Plasma Research, Department of Mathematics, Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)
1999-06-01
Chaotic dynamics may impose severe limits to deterministic modeling by dynamical equations of natural systems. We give theoretical argument that severe modeling difficulties may occur for high-dimensional chaotic systems in the sense that no model is able to produce reasonably long solutions that are realized by nature. We make these ideas concrete by investigating systems of coupled chaotic oscillators. They arise in many situations of physical and biological interests, and they also arise from discretization of nonlinear partial differential equations. {copyright} {ital 1999} {ital The American Physical Society}
Eigenfunctions in chaotic quantum systems
Energy Technology Data Exchange (ETDEWEB)
Baecker, Arnd
2007-07-01
The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted. (orig.)
Critical dimension for chaotic cosmology
Energy Technology Data Exchange (ETDEWEB)
Hosoya, Akio; Jensen, L.G.; Stein-Schabes, J.A.
1987-03-16
Using the ADM formalism for general relativity the approach to a space-time singularity of a general inhomogeneous universe, in an arbitrary number of dimensions, is studied. The question of whether chaotic behaviour is a generic feature of Einstein's equations, in an arbitrary number of dimensions, is explored. We find that models that contain ten or more spatial dimensions are non-chaotic and their approach toward the initial singularity is monotonic, whereas for those with dimensionality between four and nine their approach is chaotic. A clear geometrical picture is constructed whereby this result can be understood.
Chaotic and Arnold stripes in weakly chaotic Hamiltonian systems.
Custódio, M S; Manchein, C; Beims, M W
2012-06-01
The dynamics in weakly chaotic Hamiltonian systems strongly depends on initial conditions (ICs) and little can be affirmed about generic behaviors. Using two distinct Hamiltonian systems, namely one particle in an open rectangular billiard and four particles globally coupled on a discrete lattice, we show that in these models, the transition from integrable motion to weak chaos emerges via chaotic stripes as the nonlinear parameter is increased. The stripes represent intervals of initial conditions which generate chaotic trajectories and increase with the nonlinear parameter of the system. In the billiard case, the initial conditions are the injection angles. For higher-dimensional systems and small nonlinearities, the chaotic stripes are the initial condition inside which Arnold diffusion occurs.
Symmetric encryption algorithms using chaotic and non-chaotic generators: A review.
Radwan, Ahmed G; AbdElHaleem, Sherif H; Abd-El-Hafiz, Salwa K
2016-03-01
This paper summarizes the symmetric image encryption results of 27 different algorithms, which include substitution-only, permutation-only or both phases. The cores of these algorithms are based on several discrete chaotic maps (Arnold's cat map and a combination of three generalized maps), one continuous chaotic system (Lorenz) and two non-chaotic generators (fractals and chess-based algorithms). Each algorithm has been analyzed by the correlation coefficients between pixels (horizontal, vertical and diagonal), differential attack measures, Mean Square Error (MSE), entropy, sensitivity analyses and the 15 standard tests of the National Institute of Standards and Technology (NIST) SP-800-22 statistical suite. The analyzed algorithms include a set of new image encryption algorithms based on non-chaotic generators, either using substitution only (using fractals) and permutation only (chess-based) or both. Moreover, two different permutation scenarios are presented where the permutation-phase has or does not have a relationship with the input image through an ON/OFF switch. Different encryption-key lengths and complexities are provided from short to long key to persist brute-force attacks. In addition, sensitivities of those different techniques to a one bit change in the input parameters of the substitution key as well as the permutation key are assessed. Finally, a comparative discussion of this work versus many recent research with respect to the used generators, type of encryption, and analyses is presented to highlight the strengths and added contribution of this paper.
Kato, Tomohiro; Hasegawa, Mikio
Chaotic dynamics has been shown to be effective in improving the performance of combinatorial optimization algorithms. In this paper, the performance of chaotic dynamics in the asymmetric traveling salesman problem (ATSP) is investigated by introducing three types of heuristic solution update methods. Numerical simulation has been carried out to compare its performance with simulated annealing and tabu search; thus, the effectiveness of the approach using chaotic dynamics for driving heuristic methods has been shown. The chaotic method is also evaluated in the case of a combinatorial optimization problem in the real world, which can be solved by the same heuristic operation as that for the ATSP. We apply the chaotic method to the DNA fragment assembly problem, which involves building a DNA sequence from several hundred fragments obtained by the genome sequencer. Our simulation results show that the proposed algorithm using chaotic dynamics in a block shift operation exhibits the best performance for the DNA fragment assembly problem.
Boundary-Dependent Chaotic Regions for a Bose-Einstein Condensate Interacting with Laser Field
Institute of Scientific and Technical Information of China (English)
ZHU Qian-Quan; HAI Wen-Hua; DENG Hai-Ming
2007-01-01
Spatial chaos of a Bose-Einstein condensate perturbed by a weak laser standing wave and a weak laser S pulse is studied. By using the perturbed chaotic solution we investigate the new type of Melnikov chaotic regions, which depend on an integration constant CQ determined by the boundary conditions. It is shown that when the |c0| values are small, the chaotic region corresponds to small values of laser wave vector k, and the chaotic region for the larger k values is related to the large |c0| values. The result is confirmed numerically by finding the chaotic and regular orbits on the Poincaré section for the two different parameter regions. Thus, for a fixed c0 the adjustment of k from a small value to large value can transform the chaotic region into the regular one or on the contrary, which suggests a feasible method for eliminating or generating Melnikov chaos.
Building a Chaotic Proved Neural Network
Bahi, Jacques M; Salomon, Michel
2011-01-01
Chaotic neural networks have received a great deal of attention these last years. In this paper we establish a precise correspondence between the so-called chaotic iterations and a particular class of artificial neural networks: global recurrent multi-layer perceptrons. We show formally that it is possible to make these iterations behave chaotically, as defined by Devaney, and thus we obtain the first neural networks proven chaotic. Several neural networks with different architectures are trained to exhibit a chaotical behavior.
A new multi-scroll chaotic system
Institute of Scientific and Technical Information of China (English)
Wang Fa-Qiang; Liu Chong-Xin
2006-01-01
This paper proposes a new simple autonomous chaotic system which can generate multi-scroll chaotic attractors.The characteristic of this new multi-scroll chaotic system is that the 4n + 2m +4-scroll chaotic attractors are generated easily with n and m varying under n ≤ m. Various number of scroll chaotic attractors are illustrated not on ly by computer simulation but also by the realization of an electronic circuit experiment on EWB (Electronics Workbench).
A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems.
Horio, Yoshihiko; Ikeguchi, Tohru; Aihara, Kazuyuki
2005-01-01
We construct a mixed analog/digital chaotic neuro-computer prototype system for quadratic assignment problems (QAPs). The QAP is one of the difficult NP-hard problems, and includes several real-world applications. Chaotic neural networks have been used to solve combinatorial optimization problems through chaotic search dynamics, which efficiently searches optimal or near optimal solutions. However, preliminary experiments have shown that, although it obtained good feasible solutions, the Hopfield-type chaotic neuro-computer hardware system could not obtain the optimal solution of the QAP. Therefore, in the present study, we improve the system performance by adopting a solution construction method, which constructs a feasible solution using the analog internal state values of the chaotic neurons at each iteration. In order to include the construction method into our hardware, we install a multi-channel analog-to-digital conversion system to observe the internal states of the chaotic neurons. We show experimentally that a great improvement in the system performance over the original Hopfield-type chaotic neuro-computer is obtained. That is, we obtain the optimal solution for the size-10 QAP in less than 1000 iterations. In addition, we propose a guideline for parameter tuning of the chaotic neuro-computer system according to the observation of the internal states of several chaotic neurons in the network.
Chaotic Visual Cryptosystem Using Empirical Mode Decomposition Algorithm for Clinical EEG Signals.
Lin, Chin-Feng
2016-03-01
This paper, proposes a chaotic visual cryptosystem using an empirical mode decomposition (EMD) algorithm for clinical electroencephalography (EEG) signals. The basic design concept is to integrate two-dimensional (2D) chaos-based encryption scramblers, the EMD algorithm, and a 2D block interleaver method to achieve a robust and unpredictable visual encryption mechanism. Energy-intrinsic mode function (IMF) distribution features of the clinical EEG signal are developed for chaotic encryption parameters. The maximum and second maximum energy ratios of the IMFs of a clinical EEG signal to its refereed total energy are used for the starting points of chaotic logistic map types of encrypted chaotic signals in the x and y vectors, respectively. The minimum and second minimum energy ratios of the IMFs of a clinical EEG signal to its refereed total energy are used for the security level parameters of chaotic logistic map types of encrypted chaotic signals in the x and y vectors, respectively. Three EEG database, and seventeen clinical EEG signals were tested, and the average r and mse values are 0.0201 and 4.2626 × 10(-29), respectively, for the original and chaotically-encrypted through EMD clinical EEG signals. The chaotically-encrypted signal cannot be recovered if there is an error in the input parameters, for example, an initial point error of 0.000001 %. The encryption effects of the proposed chaotic EMD visual encryption mechanism are excellent.
Synchronization of mobile chaotic oscillator networks
Energy Technology Data Exchange (ETDEWEB)
Fujiwara, Naoya, E-mail: fujiwara@csis.u-tokyo.ac.jp [Center for Spatial Information Science, The University of Tokyo, 277-8568 Chiba (Japan); Kurths, Jürgen [Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany and Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen (United Kingdom); Díaz-Guilera, Albert [Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain and Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, Barcelona (Spain)
2016-09-15
We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.
Chaotic synchronization via linear controller
Institute of Scientific and Technical Information of China (English)
Chen Feng-Xiang; Zhang Wei-Dong
2007-01-01
A technical framework of constructing a linear controller for chaotic synchronization by utilizing the stability theory of cascade-connected system is presented. Based on the method developed in the paper, two simple and linear feedback controllers, as examples, are derived for the synchronization of Liu chaotic system and Duffing oscillator, respectively.This method is quite flexible in constructing a control law. Its effectiveness is also illustrated by the simulation results.
Chaotic diagonal recurrent neural network
Institute of Scientific and Technical Information of China (English)
Wang Xing-Yuan; Zhang Yi
2012-01-01
We propose a novel neural network based on a diagonal recurrent neural network and chaos,and its structure andlearning algorithm are designed.The multilayer feedforward neural network,diagonal recurrent neural network,and chaotic diagonal recurrent neural network are used to approach the cubic symmetry map.The simulation results show that the approximation capability of the chaotic diagonal recurrent neural network is better than the other two neural networks.
Dobrovolskis, Anthony R.; Cuzzi, Jeffrey N. (Technical Monitor)
1995-01-01
The shape and spin of Neptune's outermost satellite Nereid are still unknown. Ground-based photometry indicates large brightness variations, but different observers report very different lightcurve amplitudes and periods. On the contrary, Voyager 2 images spanning 12 days show no evidence of variations greater than 0.1 mag. The latter suggest either that Nereid is nearly spherical, or that it is rotating slowly. We propose that tides have already despun Nereid's rotation to a period of a few weeks, during the time before the capture of Triton when Nereid was closer to Neptune. Since Nereid reached its present orbit, tides have further despun Nereid to a period on the order of a month. For Nereid's orbital eccentricity of 0.75, tidal evolution ceases when the spin period is still approximately 1/8 of the orbital period. Furthermore, the synchronous resonance becomes quite weak for such high eccentricities, along with other low-order spin orbit commensurabilities. In contrast, high-order resonances become very strong particularly the 6:1, 6.5:1, 7:1, 7.5:1, and 8:1 spin states. If Nereid departs by more than approximately 1% from a sphere, however, these resonances overlap, generating chaos. Our simulations show that Nereid is likely to be in chaotic rotation for any spin period longer than about 2 weeks.
Unmasking Chaotic Attributes in Time Series of Living Cell Populations
Laurent, Michel; Deschatrette, Jean; Wolfrom, Claire M.
2010-01-01
Background Long-range oscillations of the mammalian cell proliferation rate are commonly observed both in vivo and in vitro. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes related to proliferation rate, including metabolic activity, telomere homeostasis, gene expression, and tumor growth. Methodology/Principal Findings Using a simple, original, nonlinear method based on return maps, we previously found a geometrical deterministic structure coordinating such fluctuations in populations of various cell types. However, nonlinearity and determinism are only necessary conditions for chaos; they do not by themselves constitute a proof of chaotic dynamics. Therefore, we used the same analytical method to analyze the oscillations of four well-known, low-dimensional, chaotic oscillators, originally designed in diverse settings and all possibly well-adapted to model the fluctuations of cell populations: the Lorenz, Rössler, Verhulst and Duffing oscillators. All four systems also display this geometrical structure, coordinating the oscillations of one or two variables of the oscillator. No such structure could be observed in periodic or stochastic fluctuations. Conclusion/Significance Theoretical models predict various cell population dynamics, from stable through periodically oscillating to a chaotic regime. Periodic and stochastic fluctuations were first described long ago in various mammalian cells, but by contrast, chaotic regulation had not previously been evidenced. The findings with our nonlinear geometrical approach are entirely consistent with the notion that fluctuations of cell populations can be chaotically controlled. PMID:20179755
Unmasking chaotic attributes in time series of living cell populations.
Directory of Open Access Journals (Sweden)
Michel Laurent
Full Text Available BACKGROUND: Long-range oscillations of the mammalian cell proliferation rate are commonly observed both in vivo and in vitro. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes related to proliferation rate, including metabolic activity, telomere homeostasis, gene expression, and tumor growth. METHODOLOGY/PRINCIPAL FINDINGS: Using a simple, original, nonlinear method based on return maps, we previously found a geometrical deterministic structure coordinating such fluctuations in populations of various cell types. However, nonlinearity and determinism are only necessary conditions for chaos; they do not by themselves constitute a proof of chaotic dynamics. Therefore, we used the same analytical method to analyze the oscillations of four well-known, low-dimensional, chaotic oscillators, originally designed in diverse settings and all possibly well-adapted to model the fluctuations of cell populations: the Lorenz, Rössler, Verhulst and Duffing oscillators. All four systems also display this geometrical structure, coordinating the oscillations of one or two variables of the oscillator. No such structure could be observed in periodic or stochastic fluctuations. CONCLUSION/SIGNIFICANCE: Theoretical models predict various cell population dynamics, from stable through periodically oscillating to a chaotic regime. Periodic and stochastic fluctuations were first described long ago in various mammalian cells, but by contrast, chaotic regulation had not previously been evidenced. The findings with our nonlinear geometrical approach are entirely consistent with the notion that fluctuations of cell populations can be chaotically controlled.
2006-01-01
[figure removed for brevity, see original site] Poster Version Large Magellanic Cloud This vibrant image from NASA's Spitzer Space Telescope shows the Large Magellanic Cloud, a satellite galaxy to our own Milky Way galaxy. The infrared image, a mosaic of more than 100,000 individual tiles, offers astronomers a unique chance to study the lifecycle of stars and dust in a single galaxy. Nearly one million objects are revealed for the first time in this Spitzer view, which represents about a 1,000-fold improvement in sensitivity over previous space-based missions. Most of the new objects are dusty stars of various ages populating the Large Magellanic Cloud; the rest are thought to be background galaxies. The blue color in the picture, seen most prominently in the central bar, represents starlight from older stars. The chaotic, bright regions outside this bar are filled with hot, massive stars buried in thick blankets of dust. The red clouds contain cooler interstellar gas and molecular-sized dust grains illuminated by ambient starlight. The Large Magellanic Cloud, located 160,000 light-years from Earth, is one of a handful of dwarf galaxies that orbit our own Milky Way. It is approximately one-third as wide as the Milky Way, and, if it could be seen in its entirety, would cover the same amount of sky as a grid of about 480 full moons. About one-third of the whole galaxy can be seen in the Spitzer image. This picture is a composite of infrared light captured by Spitzer's infrared array camera. Light with wavelengths of 8 and 5.8 microns is red and orange: 4.5-micron light is green; and 3.6-micron light is blue.
How chaotic are strange non-chaotic attractors?
Glendinning, Paul; Jäger, Tobias H.; Keller, Gerhard
2006-09-01
We show that the classic examples of quasiperiodically forced maps with strange non-chaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit sensitive dependence on initial conditions, both on the whole phase space and restricted to the attractor. The results also remain valid in more general classes of quasiperiodically forced systems. Further, we include an elementary proof of a classic result by Glasner and Weiss on sensitive dependence, and we clarify the structure of the attractor in an example with two-dimensional fibres also introduced by Grebogi et al.
On the Design of Chaotic Oscillators
DEFF Research Database (Denmark)
Lindberg, Erik; Tamasevicius, A; Cenys, A.
1998-01-01
A discussion of the chaotic oscillator concept from a design methodology pointof view. The attributes of some chaoticoscillators are discussed and a systematicdesign method based on eigenvalue investigation is proposed. The method isillustrated with a chaotic Wien-bridgeoscillator design....
Intermittent chaotic chimeras for coupled rotators
DEFF Research Database (Denmark)
Olmi, Simona; Martens, Erik Andreas; Thutupalli, Shashi
2015-01-01
Two symmetrically coupled populations of N oscillators with inertia m display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendulums. In particular, we report evidence of intermittent chaotic chimeras, where one population is synchronized and the other...
Decoherence, entanglement decay, and equilibration produced by chaotic environments.
Lemos, Gabriela Barreto; Toscano, Fabricio
2011-07-01
We investigate decoherence in quantum systems coupled via dephasing-type interactions to an arbitrary environment with chaotic underlying classical dynamics. The coherences of the reduced state of the central system written in the preferential energy eigenbasis are quantum Loschmidt echoes, which in the strong coupling regime are characterized at long time scales by fluctuations around a constant mean value. We show that due to the chaotic dynamics of the environment, the mean value and the width of the Loschmidt-echo fluctuations are inversely proportional to the quantity we define as the effective Hilbert-space dimension of the environment, which in general is smaller than the dimension of the entire available Hilbert space. Nevertheless, in the semiclassical regime this effective Hilbert-space dimension is in general large, in which case even a chaotic environment with few degrees of freedom produces decoherence without revivals. Moreover we show that in this regime the environment leads the central system to equilibrate to the time average of its reduced density matrix, which corresponds to a diagonal state in the preferential energy eigenbasis. For the case of two uncoupled, initially entangled central systems that interact with identical local quantum environments with chaotic underlying classical dynamics, we show that in the semiclassical limit the equilibration state is arbitrarily close to a separable state. We confirm our results with numerical simulations in which the environment is modeled by the quantum kicked rotor in the chaotic regime.
Detecting variation in chaotic attractors.
Carroll, T L
2011-06-01
If the output of an experiment is a chaotic signal, it may be useful to detect small changes in the signal, but there are a limited number of ways to compare signals from chaotic systems, and most known methods are not robust in the presence of noise. One may calculate dimension or Lyapunov exponents from the signal, or construct a synchronizing model, but all of these are only useful in low noise situations. I introduce a method for detecting small variations in a chaotic attractor based on directly calculating the difference between vector fields in phase space. The differences are found by comparing close strands in phase space, rather than close neighbors. The use of strands makes the method more robust to noise and more sensitive to small attractor differences.
Chaotic Synchronzation System and Electrocardiogram
Institute of Scientific and Technical Information of China (English)
LiuqingPei; XinlaiDai; 等
1997-01-01
A mathematical model of chaotic synchronization of the heart-blood flow coupling dynamics is propsed,which is based on a seven dimension nonlinear dynamical system constructed by three subsystems of the sinoatrial node natural pacemaker,the cardiac relaxation oscillator and the dynamics of blood-fluid in heart chambers.The existence and robustness of the self-chaotic synchronization of the system are demonstrated by both methods of theoretical analysis and numerical simulation.The spectrum of Lyapunov exponent,the Lyapunov dimension and the Kolmogorov entropy are estimated when the system was undergoing the state of self-chaotic synchronization evolution.The time waveform of the dynamical variable,which represents the membrane potential of the cardiac integrative cell,shows a shape which is similar to that of the normal electrocardiogram(ECG) of humans,thus implying that the model possesses physiological significance functionally.
Chaotic eigenfunctions in phase space
Nonnenmacher, S
1997-01-01
We study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic. In order to analyze their semiclassical behavior, we use the Bargmann-Husimi representations for quantum states, as well as their stellar parametrization, which encodes states through a minimal set of points in phase space (the constellation of zeros of the Husimi density). We rigorously prove that a semiclassical uniform distribution of Husimi densities on the torus entails a similar equidistribution for the corresponding constellations. We deduce from this property a universal behavior for the phase patterns of chaotic Bargmann eigenfunctions, which reminds of the WKB approximation for eigenstates of integrable systems (though in a weaker sense). In order to obtain more precise information on ``chaotic eigenconstellations", we then model their properties by ensembles of random states, generalizing former results on the 2-sphere to the torus geometry. This approach yields statistical predictions fo...
The Statistics of Chaotic Tunnelling
Creagh, S C; Creagh, Stephen C.; Whelan, Niall D.
2000-01-01
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on using the properties of a semiclassical tunnelling operator together with random matrix theory arguments about wave function overlaps. The resulting distribution depends on the stability of a specific tunnelling orbit and is therefore not universal. However it does reduce to the universal Porter-Thomas form as the orbit becomes very unstable. For some choices of system parameters there are systematic deviations which we explain in terms of scarring of certain real periodic orbits. The theory is tested in a model symmetric double well problem and possible experimental realisations are discussed.
Communication Scheme via Cascade Chaotic Systems
Institute of Scientific and Technical Information of China (English)
HUA Chang-Chun; GUAN Xin-Ping
2004-01-01
@@ A new chaotic communication scheme is constructed. Different from the existing literature, cascade chaotic systems are employed. Two cascade modes are considered. First, we investigate the input to state cascade mode;cascade systems between different kinds of chaotic systems are considered. Then the parameter cascade case of chaotic system is studied. Under the different cases, the corresponding receivers are designed, which can succeed in recovering the former emitted signal. Simulations are performed to verify the validity of the proposed main results.
Impulsive Synchronization of Discrete Chaotic Systems
Institute of Scientific and Technical Information of China (English)
郑永爱; 年漪蓓; 刘曾荣
2003-01-01
Impulsive synchronization of two chaotic maps is reformulated as impulsive control of the synchronization error system. We then present a theorem on the asymptotic synchronization of two chaotic maps by using synchronization impulses with varying impulsive intervals. As an example and application of the theorem, we derives some sufficient conditions for the synchronization of two chaotic Lozi maps via impulsive control. The effectiveness of this approach has been demonstrated with chaotic Lozi map.
A new multi-scroll chaotic generator
Institute of Scientific and Technical Information of China (English)
Wang Fa-Qiang; Liu Chong-Xin
2007-01-01
In this paper a new simple multi-scroll chaotic generator is studied. The characteristic of this new multi-scroll chaotic generator is that it is easy to generate different number of scroll chaotic attractors through modifying the nature number n after fixing the suitable system parameters and it does not need complex mathematical derivation. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on Electronic Workbench (EWB).
Chaotic Encryption Method Based on Life-Like Cellular Automata
Machicao, Marina Jeaneth; Bruno, Odemir M
2011-01-01
We propose a chaotic encryption method based on Cellular Automata(CA), specifically on the family called the "Life-Like" type. Thus, the encryption process lying on the pseudo-random numbers generated (PRNG) by each CA's evolution, which transforms the password as the initial conditions to encrypt messages. Moreover, is explored the dynamical behavior of CA to reach a "good" quality as PRNG based on measures to quantify "how chaotic a dynamical system is", through the combination of the entropy, Lyapunov exponent, and Hamming distance. Finally, we present the detailed security analysis based on experimental tests: DIEHARD and ENT suites, as well as Fouriers Power Spectrum, used as a security criteria.
Quantum Computing, $NP$-complete Problems and Chaotic Dynamics
Ohya, M; Ohya, Masanori; Volovich, Igor V.
1999-01-01
An approach to the solution of NP-complete problems based on quantumcomputing and chaotic dynamics is proposed. We consider the satisfiabilityproblem and argue that the problem, in principle, can be solved in polynomialtime if we combine the quantum computer with the chaotic dynamics amplifierbased on the logistic map. We discuss a possible implementation of such achaotic quantum computation by using the atomic quantum computer with quantumgates described by the Hartree-Fock equations. In this case, in principle, onecan build not only standard linear quantum gates but also nonlinear gates andmoreover they obey to Fermi statistics. This new type of entaglement relatedwith Fermi statistics can be interesting also for quantum communication theory.
Image encryption based on new Beta chaotic maps
Zahmoul, Rim; Ejbali, Ridha; Zaied, Mourad
2017-09-01
In this paper, we created new chaotic maps based on Beta function. The use of these maps is to generate chaotic sequences. Those sequences were used in the encryption scheme. The proposed process is divided into three stages: Permutation, Diffusion and Substitution. The generation of different pseudo random sequences was carried out to shuffle the position of the image pixels and to confuse the relationship between the encrypted the original image, so that significantly increasing the resistance to attacks. The acquired results of the different types of analysis indicate that the proposed method has high sensitivity and security compared to previous schemes.
k Spectrum of Passive Scalars in Lagrangian Chaotic Fluid Flows
Antonsen, Thomas M., Jr.; Fan, Zhencan Frank; Ott, Edward
1995-08-01
An eikonal-type description for the evolution of k spectra of passive scalars convected in a Lagrangian chaotic fluid flow is shown to accurately reproduce results from orders of magnitude more time consuming computations based on the full passive scalar partial differential equation. Furthermore, the validity of the reduced description, combined with concepts from chaotic dynamics, allows new theoretical results on passive scalar k spectra to be obtained. Illustrative applications are presented to long-time passive scalar decay, and to Batchelor's law k spectrum and its diffusive cutoff.
Esfandiari, Kasra; Abdollahi, Farzaneh; Talebi, Heidar Ali
2015-10-01
This paper presents a tracking control methodology for a class of uncertain nonlinear systems subject to input saturation constraint and external disturbances. Unlike most previous approaches on saturated systems, which assumed affine nonlinear systems, in this paper, tracking control problem is solved for uncertain nonaffine nonlinear systems with input saturation. To deal with the saturation constraint, an auxiliary system is constructed and a modified tracking error is defined. Then, by employing implicit function theorem, mean value theorem, and modified tracking error, updating rules are derived based on the well-known back-propagation (BP) algorithm, which has been proven to be the most relevant updating rule to control problems. However, most of the previous approaches on BP algorithm suffer from lack of stability analysis. By injecting a damping term to the standard BP algorithm, uniformly ultimately boundedness of all the signals of the closed-loop system is ensured via Lyapunov's direct method. Furthermore, the presented approach employs nonlinear in parameter neural networks. Hence, the proposed scheme is applicable to systems with higher degrees of nonlinearity. Using a high-gain observer to reconstruct the states of the system, an output feedback controller is also presented. Finally, the simulation results performed on a Duffing-Holmes chaotic system, a generalized pendulum-type system, and a numerical system are presented to demonstrate the effectiveness of the suggested state and output feedback control schemes.
Chaotic zones around gravitating binaries
Shevchenko, Ivan I
2014-01-01
The extent of the continuous zone of chaotic orbits of a small-mass tertiary around a system of two gravitationally bound bodies (a double star, a double black hole, a binary asteroid, etc.) is estimated analytically, in function of the tertiary's orbital eccentricity. The separatrix map theory is used to demonstrate that the central continuous chaos zone emerges due to overlapping of the orbital resonances corresponding to the integer ratios p:1 between the tertiary and the binary periods. The binary's mass ratio, above which such a chaotic zone is universally present, is also estimated.
Modeling of deterministic chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Lai, Y. [Department of Physics and Astronomy and Department of Mathematics, The University of Kansas, Lawrence, Kansas 66045 (United States); Grebogi, C. [Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States); Grebogi, C.; Kurths, J. [Department of Physics and Astrophysics, Universitaet Potsdam, Postfach 601553, D-14415 Potsdam (Germany)
1999-03-01
The success of deterministic modeling of a physical system relies on whether the solution of the model would approximate the dynamics of the actual system. When the system is chaotic, situations can arise where periodic orbits embedded in the chaotic set have distinct number of unstable directions and, as a consequence, no model of the system produces reasonably long trajectories that are realized by nature. We argue and present physical examples indicating that, in such a case, though the model is deterministic and low dimensional, statistical quantities can still be reliably computed. {copyright} {ital 1999} {ital The American Physical Society}
Theoretical Investigations of Chaotic Dynamics
1993-10-31
INVESTIGATIONS OF CHAOTIC DYNAMICS" PROFESSOR JAMES A YORKE CELSO GREBOGI UNIVERSITY OF MARYLAND COLLEGE PARK MD 20742-2431 F49620-92-J-0033 I PREFACE This...publication. d. "Evolution of Attractor Boundaries of Two-Dimensional Noninvertible Maps", W. Chin, I. Kan and C. Grebogi , Random & Comp. Dyn. L 349-370...1993). e "How often are chaotic saddles nonhyperbolic?", Y-C. Lai, C. Grebogi , and J. A Yorke, Nonlinearity, 6., 779-797 (1993). f. "A Geometric
Chaotic signals in digital communications
Eisencraft, Marcio; Suyama, Ricardo
2013-01-01
Chaotic Signals in Digital Communications combines fundamental background knowledge with state-of-the-art methods for using chaotic signals and systems in digital communications. The book builds a bridge between theoretical works and practical implementation to help researchers attain consistent performance in realistic environments. It shows the possible shortcomings of the chaos-based communication systems proposed in the literature, particularly when they are subjected to non-ideal conditions. It also presents a toolbox of techniques for researchers working to actually implement such system
Lectures on chaotic dynamical systems
Afraimovich, Valentin
2002-01-01
This book is devoted to chaotic nonlinear dynamics. It presents a consistent, up-to-date introduction to the field of strange attractors, hyperbolic repellers, and nonlocal bifurcations. The authors keep the highest possible level of "physical" intuition while staying mathematically rigorous. In addition, they explain a variety of important nonstandard algorithms and problems involving the computation of chaotic dynamics. The book will help readers who are not familiar with nonlinear dynamics to understand and appreciate sophisticated modern dynamical systems and chaos. Intended for courses in either mathematics, physics, or engineering, prerequisites are calculus, differential equations, and functional analysis.
Observers for a Class of Chaotic Systems
Institute of Scientific and Technical Information of China (English)
ZHOU Ping
2006-01-01
The design of observers for a class of practical physical chaotic systems is discussed.By using only one state variable and its time derivatives,a control law is constructed to achieve the synchronization between the investigated chaotic systems and their observers,and the results are proved theoretically.Several observers of chaotic systems are designed by using this method.
Synchronization in driven chaotic systems: Diagnostics and bifurcations
DEFF Research Database (Denmark)
Vadivasova, T.E.; Balanov, A.G.; Sosnovtseva, O.V.;
1999-01-01
We investigate generic aspects of chaos synchronization in an externally forced Rössler system. By comparing different diagnostic methods, we show the existence of a well-defined cut-off of synchronization associated with the transition from weak to fully developed chaos. Two types of chaotic beh...... behavior, differing by the number of vanishing Lyapunov exponents, are observed outside the synchronization regime....
Institute of Scientific and Technical Information of China (English)
Yu Fei; Wang Chun-Hua; Yin Jin-Wen; Xu Hao
2011-01-01
In this paper,we propose a novel four-dimensional autonomous chaotic system.Of particular interest is that this novel system can generate one-,two,three- and four-wing chaotic attractors with the variation of a single parameter,and the multi-wing type of the chaotic attractors can be displayed in all directions.The system is simple with a large positive Lyapunov exponent and can exhibit some interesting and complicated dynamical behaviours.Basic dynamical properties of the four-dimensional chaotic system,such as equilibrium points,the Poincaré map,the bifurcation diagram and the Lyapunov exponents are investigated by using either theoretical analysis or numerical method.Finally,a circuit is designed for the implementation of the multi-wing chaotic attractors.The electronic workbench observations are in good agreement with the numerical simulation results.
Chaotic domains: A numerical investigation
Cross, M. C.; Meiron, D.; Tu, Yuhai
1994-01-01
We study the chaotic domain state in rotating convection using a model equation that allows for a continuous range of roll orientations as in the experimental system. Methods are developed for extracting the domain configuration from the resulting patterns that should be applicable to a wide range of domain states. Comparison with the truncated three mode amplitude equation description is made.
Chaotic Dispersal of Tidal Debris
Price-Whelan, Adrian M; Valluri, Monica; Pearson, Sarah; Kupper, Andreas H W; Hogg, David W
2015-01-01
Several long, dynamically cold stellar streams have been observed around the Milky Way Galaxy, presumably formed from the tidal disruption of globular clusters. In integrable potentials---where all orbits are dynamically regular---tidal debris phase-mixes close to the orbit of the progenitor system. However, cosmological simulations of structure formation suggest that the Milky Way's dark matter halo is expected not to be fully integrable; an appreciable fraction of orbits will be chaotic. This paper examines the influence of chaos on the phase-space morphology of cold tidal streams. We find very stark results: Streams in chaotic regions look very different from those in regular regions. We find that streams (simulated using test particle ensembles of nearby orbits) can be sensitive to chaos on a much shorter time-scale than any standard prediction (from the Lyapunov or frequency-diffusion times). For example, on a weakly chaotic orbit with a chaotic timescale predicted to be >1000 orbital periods (>1000 Gyr)...
Learning in a Chaotic Environment
Goldman, Ellen; Plack, Margaret; Roche, Colleen; Smith, Jeffrey; Turley, Catherine
2009-01-01
Purpose: The purpose of this study is to understand how, when, and why emergency medicine residents learn while working in the chaotic environment of a hospital emergency room. Design/methodology/approach: This research used a qualitative interview methodology with thematic data analysis that was verified with the entire population of learners.…
Chaotic dynamics, fluctuations, nonequilibrium ensembles.
Gallavotti, Giovanni
1998-06-01
The ideas and the conceptual steps leading from the ergodic hypothesis for equilibrium statistical mechanics to the chaotic hypothesis for equilibrium and nonequilibrium statistical mechanics are illustrated. The fluctuation theorem linear law and universal slope prediction for reversible systems is briefly derived. Applications to fluids are briefly alluded to. (c) 1998 American Institute of Physics.
Visibility graphlet approach to chaotic time series
Energy Technology Data Exchange (ETDEWEB)
Mutua, Stephen [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Computer Science Department, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega (Kenya); Gu, Changgui, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn; Yang, Huijie, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China)
2016-05-15
Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems. Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.
Advances and applications in chaotic systems
Volos, Christos
2016-01-01
This book reports on the latest advances and applications of chaotic systems. It consists of 25 contributed chapters by experts who are specialized in the various topics addressed in this book. The chapters cover a broad range of topics of chaotic systems such as chaos, hyperchaos, jerk systems, hyperjerk systems, conservative and dissipative systems, circulant chaotic systems, multi-scroll chaotic systems, finance chaotic system, highly chaotic systems, chaos control, chaos synchronization, circuit realization and applications of chaos theory in secure communications, mobile robot, memristors, cellular neural networks, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in chaos theory. This book will serve as a reference book for graduate students and researchers with a basic knowledge of chaos theory and control systems. The resulting design procedures on the chaotic systems are emphasized using MATLAB software.
Visibility graphlet approach to chaotic time series.
Mutua, Stephen; Gu, Changgui; Yang, Huijie
2016-05-01
Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems. Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.
Applications of tripled chaotic maps in cryptography
Energy Technology Data Exchange (ETDEWEB)
Behnia, S. [Department of Physics, IAU, Urmia (Iran, Islamic Republic of)], E-mail: s.behnia@iaurmia.ac.ir; Akhshani, A. [School of Physics, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia); Akhavan, A. [School of Computer Science, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia); Mahmodi, H. [School of Physics, Universiti Sains Malaysia, 11800 USM, Penang (Malaysia)
2009-04-15
Security of information has become a major issue during the last decades. New algorithms based on chaotic maps were suggested for protection of different types of multimedia data, especially digital images and videos in this period. However, many of them fundamentally were flawed by a lack of robustness and security. For getting higher security and higher complexity, in the current paper, we introduce a new kind of symmetric key block cipher algorithm that is based on tripled chaotic maps. In this algorithm, the utilization of two coupling parameters, as well as the increased complexity of the cryptosystem, make a contribution to the development of cryptosystem with higher security. In order to increase the security of the proposed algorithm, the size of key space and the computational complexity of the coupling parameters should be increased as well. Both the theoretical and experimental results state that the proposed algorithm has many capabilities such as acceptable speed and complexity in the algorithm due to the existence of two coupling parameters and high security. Note that the ciphertext has a flat distribution and has the same size as the plaintext. Therefore, it is suitable for practical use in secure communications.
Identification of Chaotic Systems with Application to Chaotic Communication
Institute of Scientific and Technical Information of China (English)
FENG Jiu-Chao; QIU Yu-Hui
2004-01-01
@@ We propose and develop a novel method to identify a chaotic system with time-varying bifurcation parameters via an observation signal which has been contaminated by additive white Gaussian noise. This method is based on an adaptive algorithm, which takes advantage of the good approximation capability of the radial basis function neural network and the ability of the extended Kalman filter for tracking a time-varying dynamical system. It is demonstrated that, provided the bifurcation parameter varies slowly in a time window, a chaotic dynamical system can be tracked and identified continuously, and the time-varying bifurcation parameter can also be retrieved in a sub-window of time via a simple least-square-fit method.
All-optical chaotic MQW laser repeater for long-haul chaotic communications
Institute of Scientific and Technical Information of China (English)
Senlin Yan
2005-01-01
We present an all-optical chaotic multi-quantum-well (MQW) laser repeater system to be used in long-haul chaotic communications. Chaotic synchronization is achieved among transmitter, repeater, and receiver. Chaotic repeater communications with a sinusoidal signal of 0.2-GHz modulation frequency and a digital signal of 0.4-Gb/s bit rate are numerically simulated, respectively. Calculation results illustrate that the signals are well decoded by the chaotic repeaters. Its bandwidth and the characteristics at much high bit rate are also analyzed. Simulation shows that the repeater can improve decoding quality, especially in higher bit rate chaotic communications.
Recovering chaotic properties from small data.
Shao, Chenxi; Fang, Fang; Liu, Qingqing; Wang, Tingting; Wang, Binghong; Yin, Peifeng
2014-12-01
Physical properties are obviously essential to study a chaotic system that generates discrete-time signals, but recovering chaotic properties of a signal source from small data is a very troublesome work. Existing chaotic models are weak in dealing with such case in that most of them need big data to exploit those properties. In this paper, geometric theory is considered to solve this problem. We build a smooth trajectory from series to implicitly exhibit the chaotic properties with series-nonuniform rational B-spline (S-NURBS) modeling method, which is presented by our team to model slow-changing chaotic time series. As for the part of validation, we reveal how well our model recovers the properties from both the statistical and the chaotic aspects to confirm the effectiveness of the model. Finally a practical chaotic model is built up to recover the chaotic properties contained in the Musa standard dataset, which is used in analyzing software reliability, thereby further proves the high credibility of this model in practical time series. The effectiveness of the S-NURBS modeling leads us to believe that it is really a feasible and worthy research area to study chaotic systems from geometric perspective. For this reason, we reckon that we have opened up a new horizon for chaotic system research.
Illusion optics in chaotic light
Zhang, Su-Heng; Gan, Shu; Xiong, Jun; Zhang, Xiangdong; Wang, Kaige
2010-08-01
The time-reversal process provides the possibility to counteract the time evolution of a physical system. Recent research has shown that such a process can occur in the first-order field correlation of chaotic light and result in the spatial interference and phase-reversal diffraction in an unbalanced interferometer. Here we report experimental investigations on the invisibility cloak and illusion phenomena in chaotic light. In an unbalanced interferometer illuminated by thermal light, we have observed the cloak effect and the optical transformation of one object into another object. The experimental results can be understood by the phase-reversal diffraction, and they demonstrate the theoretical proposal of similar effects in complementary media.
Chaotic attractors with separated scrolls
Energy Technology Data Exchange (ETDEWEB)
Bouallegue, Kais, E-mail: kais-bouallegue@yahoo.fr [Department of Electrical Engineering, Higher Institute of Applied Sciences and Technology of Sousse, Sousse (Tunisia)
2015-07-15
This paper proposes a new behavior of chaotic attractors with separated scrolls while combining Julia's process with Chua's attractor and Lorenz's attractor. The main motivation of this work is the ability to generate a set of separated scrolls with different behaviors, which in turn allows us to choose one or many scrolls combined with modulation (amplitude and frequency) for secure communication or synchronization. This set seems a new class of hyperchaos because each element of this set looks like a simple chaotic attractor with one positive Lyapunov exponent, so the cardinal of this set is greater than one. This new approach could be used to generate more general higher-dimensional hyperchaotic attractor for more potential application. Numerical simulations are given to show the effectiveness of the proposed theoretical results.
The convergence of chaotic integrals
Bauer, O; Bauer, Oliver; Mainieri, Ronnie
1995-01-01
We review the convergence of chaotic integrals computed by Monte Carlo simulation, the trace method, dynamical zeta function, and Fredholm determinant on a simple one-dimensional example: the parabola repeller. There is a dramatic difference in convergence between these approaches. The convergence of the Monte Carlo method follows an inverse power law, whereas the trace method and dynamical zeta function converge exponentially, and the Fredholm determinant converges faster than any exponential.
Chaotic behavior in dopamine neurodynamics.
King, R; Barchas, J.D.; Huberman, B A
1984-01-01
We report the results of the dynamics of a model of the central dopaminergic neuronal system. In particular, for certain values of a parameter k, which monitors the efficacy of dopamine at the postsynaptic receptor, chaotic solutions of the dynamical equations appear--a prediction that correlates with the observed increased variability in behavior among schizophrenics, the rapid fluctuations in motor activity among Parkinsonian patients treated chronically with L-dopa, and the lability of moo...
Chaotic principle an experimental test
Bonetto, F; Garrido, P L
1996-01-01
The chaotic hypothesis discussed in [GC1] is tested experimentally in a simple conduction model. Besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which, as the forcing strength grows, the attractor ceases to be an Anosov system and becomes an Axiom A attractor. A first test of the new predictions is also attempted.
Design and implementation of a novel multi-scroll chaotic system
Institute of Scientific and Technical Information of China (English)
Zhang Chao-Xia; Yu Si-Min
2009-01-01
This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by constructing triangular wave, sawtooth wave and hysteresis sequence. The presented new multi-scroll chaotic system is different from the classical multi-scroll chaotic Chua system in dimensionless state equations, nonlinear functions and maximum Lyapunov exponents. In addition, the basic dynamical behaviours, including equilibrium points, eigenvalues, eigenvectors, eigenplanes, bifurcation diagrams and Lyapunov exponents, are further investigated. The success of the design is illustrated by both numerical simulations and circuit experiments.
CHAOTIC ZONES AROUND GRAVITATING BINARIES
Energy Technology Data Exchange (ETDEWEB)
Shevchenko, Ivan I., E-mail: iis@gao.spb.ru [Pulkovo Observatory of the Russian Academy of Sciences, Pulkovskoje ave. 65, St. Petersburg 196140 (Russian Federation)
2015-01-20
The extent of the continuous zone of chaotic orbits of a small-mass tertiary around a system of two gravitationally bound primaries of comparable masses (a binary star, a binary black hole, a binary asteroid, etc.) is estimated analytically, as a function of the tertiary's orbital eccentricity. The separatrix map theory is used to demonstrate that the central continuous chaos zone emerges (above a threshold in the primaries' mass ratio) due to overlapping of the orbital resonances corresponding to the integer ratios p:1 between the tertiary and the central binary periods. In this zone, the unlimited chaotic orbital diffusion of the tertiary takes place, up to its ejection from the system. The primaries' mass ratio, above which such a chaotic zone is universally present at all initial eccentricities of the tertiary, is estimated. The diversity of the observed orbital configurations of biplanetary and circumbinary exosystems is shown to be in accord with the existence of the primaries' mass parameter threshold.
Kuusela, Tom A.
2017-09-01
A He-Ne laser is an example of a class A laser, which can be described by a single nonlinear differential equation of the complex electric field. This laser system has only one degree of freedom and is thus inherently stable. A He-Ne laser can be driven to the chaotic condition when a large fraction of the output beam is injected back to the laser. In practice, this can be done simply by adding an external mirror. In this situation, the laser system has infinite degrees of freedom and therefore it can have a chaotic attractor. We show the fundamental laser equations and perform elementary stability analysis. In experiments, the laser intensity variations are measured by a simple photodiode circuit. The laser output intensity time series is studied using nonlinear analysis tools which can be found freely on the internet. The results show that the laser system with feedback has an attractor of a reasonably high dimension and that the maximal Lyapunov exponent is positive, which is clear evidence of chaotic behaviour. The experimental setup and analysis steps are so simple that the studies can even be implemented in the undergraduate physics laboratory.
Digital Communication Using Chaotic Pulse Generators
Rulkov, N F; Tsimring, L S; Volkovskii, A R; Abarbanel, Henry D I; Larson, L; Yao, K
1999-01-01
Utilization of chaotic signals for covert communications remains a very promising practical application. Multiple studies indicated that the major shortcoming of recently proposed chaos-based communication schemes is their susceptibility to noise and distortions in communication channels. In this talk we discuss a new approach to communication with chaotic signals, which demonstrates good performance in the presence of channel distortions. This communication scheme is based upon chaotic signals in the form of pulse trains where intervals between the pulses are determined by chaotic dynamics of a pulse generator. The pulse train with chaotic interpulse intervals is used as a carrier. Binary information is modulated onto this carrier by the pulse position modulation method, such that each pulse is either left unchanged or delayed by a certain time, depending on whether ``0'' or ``1'' is transmitted. By synchronizing the receiver to the chaotic pulse train we can anticipate the timing of pulses corresponding to ...
Confined chaotic behavior in collective motion for populations of globally coupled chaotic elements
Nakagawa, N; Nakagawa, Naoko; Komatsu, Teruhisa S.
1999-01-01
The Lyapunov exponent for collective motion is defined in order to characterize chaotic properties of collective motion for large populations of chaotic elements. Numerical computations for this quantity suggest that such collective motion is always chaotic, whenever it appears. Chaotic behavior of collective motion is found to be confined within a small scale, whose size is estimated using the value of the Lyapunov exponent. Finally, we conjecture why the collective motion appears low dimensional despite the actual high dimensionality of the dynamics.
Synchronization of chaotic systems with parameter driven by a chaotic signal
Energy Technology Data Exchange (ETDEWEB)
Li Guohui [Department of Communication Engineering, Shanghai University, Yanchang Road 149, Shanghai 200072 (China)] e-mail: ghlee@shl63.net
2005-12-01
Chaos control with driving parameter scheme in uncoupled identical chaotic oscillators is presented. By driving the parameter of chaotic systems using external chaotic signal, synchronization and anti-synchronization can be implemented. Numerical simulations show that either synchronization or anti-synchronization can appear depending significantly on initial condition and on driving strength. The proposed method is particularly suited for a variety of chaotic systems, which cannot couple with each other in engineering.
Output Regulation of the Arneodo Chaotic System
Sundarapandian Vaidyanathan
2010-01-01
This paper solves the problem of regulating the output of the Arneodo chaotic system (1981), which is one of the paradigms of chaotic dynamical systems. Explicitly, using the state feedback control laws, the output of the Arneodo chaotic system is regulated so as to track constant reference signals as well as to track periodic reference signals. The control laws are derived using the regulator equations of Byrnes and Isidori (1990), which provide the solution of the output regulation problem ...
Intermittent chaotic chimeras for coupled rotators.
Olmi, Simona; Martens, Erik A; Thutupalli, Shashi; Torcini, Alessandro
2015-09-01
Two symmetrically coupled populations of N oscillators with inertia m display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendulums. In particular, we report evidence of intermittent chaotic chimeras, where one population is synchronized and the other jumps erratically between laminar and turbulent phases. These states have finite lifetimes diverging as a power law with N and m. Lyapunov analyses reveal chaotic properties in quantitative agreement with theoretical predictions for globally coupled dissipative systems.
Chaotic evolution of the solar system
Sussman, Gerald J.; Wisdom, Jack
1992-01-01
The evolution of the entire planetary system has been numerically integrated for a time span of nearly 100 million years. This calculation confirms that the evolution of the solar system as a whole is chaotic, with a time scale of exponential divergence of about 4 million years. Additional numerical experiments indicate that the Jovian planet subsystem is chaotic, although some small variations in the model can yield quasi-periodic motion. The motion of Pluto is independently and robustly chaotic.
Robust synchronization of chaotic systems via feedback
Energy Technology Data Exchange (ETDEWEB)
Femat, Ricardo [IPICYT, San Luis Potosi (Mexico). Dept. de Matematicas Aplicadas; Solis-Perales, Gualberto [Universidad de Guadalajara, Centro Univ. de Ciencias Exactas e Ingenierias (Mexico). Div. de Electronica y Computacion
2008-07-01
This volume includes the results derived during last ten years about both suppression and synchronization of chaotic -continuous time- systems. Along this time, the concept was to study how the intrinsic properties of dynamical systems can be exploited to suppress and to synchronize the chaotic behaviour and what synchronization phenomena can be found under feedback interconnection. A compilation of these findings is described in this book. This book shows a perspective on synchronization of chaotic systems. (orig.)
Gu, Huaguang
2013-06-01
The transition from chaotic bursting to chaotic spiking has been simulated and analyzed in theoretical neuronal models. In the present study, we report experimental observations in a neural pacemaker of a transition from chaotic bursting to chaotic spiking within a bifurcation scenario from period-1 bursting to period-1 spiking. This was induced by adjusting extracellular calcium or potassium concentrations. The bifurcation scenario began from period-doubling bifurcations or period-adding sequences of bursting pattern. This chaotic bursting is characterized by alternations between multiple continuous spikes and a long duration of quiescence, whereas chaotic spiking is comprised of fast, continuous spikes without periods of quiescence. Chaotic bursting changed to chaotic spiking as long interspike intervals (ISIs) of quiescence disappeared within bursting patterns, drastically decreasing both ISIs and the magnitude of the chaotic attractors. Deterministic structures of the chaotic bursting and spiking patterns are also identified by a short-term prediction. The experimental observations, which agree with published findings in theoretical neuronal models, demonstrate the existence and reveal the dynamics of a neuronal transition from chaotic bursting to chaotic spiking in the nervous system.
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale
Energy Technology Data Exchange (ETDEWEB)
Maslennikov, Oleg V.; Nekorkin, Vladimir I. [Institute of Applied Physics of RAS, Nizhny Novgorod (Russian Federation)
2016-07-15
In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale.
Maslennikov, Oleg V; Nekorkin, Vladimir I
2016-07-01
In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.
Transmission Error and Compression Robustness of 2D Chaotic Map Image Encryption Schemes
Directory of Open Access Journals (Sweden)
Michael Gschwandtner
2007-11-01
Full Text Available This paper analyzes the robustness properties of 2D chaotic map image encryption schemes. We investigate the behavior of such block ciphers under different channel error types and find the transmission error robustness to be highly dependent on on the type of error occurring and to be very different as compared to the effects when using traditional block ciphers like AES. Additionally, chaotic-mixing-based encryption schemes are shown to be robust to lossy compression as long as the security requirements are not too high. This property facilitates the application of these ciphers in scenarios where lossy compression is applied to encrypted material, which is impossible in case traditional ciphers should be employed. If high security is required chaotic mixing loses its robustness to transmission errors and compression, still the lower computational demand may be an argument in favor of chaotic mixing as compared to traditional ciphers when visual data is to be encrypted.
Transmission Error and Compression Robustness of 2D Chaotic Map Image Encryption Schemes
Directory of Open Access Journals (Sweden)
Gschwandtner Michael
2007-01-01
Full Text Available This paper analyzes the robustness properties of 2D chaotic map image encryption schemes. We investigate the behavior of such block ciphers under different channel error types and find the transmission error robustness to be highly dependent on on the type of error occurring and to be very different as compared to the effects when using traditional block ciphers like AES. Additionally, chaotic-mixing-based encryption schemes are shown to be robust to lossy compression as long as the security requirements are not too high. This property facilitates the application of these ciphers in scenarios where lossy compression is applied to encrypted material, which is impossible in case traditional ciphers should be employed. If high security is required chaotic mixing loses its robustness to transmission errors and compression, still the lower computational demand may be an argument in favor of chaotic mixing as compared to traditional ciphers when visual data is to be encrypted.
Identification of fractional chaotic system parameters
Energy Technology Data Exchange (ETDEWEB)
Al-Assaf, Yousef E-mail: yassaf@aus.ac.ae; El-Khazali, Reyad E-mail: khazali@ece.ac.ae; Ahmad, Wajdi E-mail: wajdi@sharjah.ac.ae
2004-11-01
In this work, a technique is introduced for parameter identification of fractional order chaotic systems. Features are extracted, from chaotic system outputs obtained for different system parameters, using discrete Fourier transform (DFT), power spectral density (PSD), and wavelets transform (WT). Artificial neural networks (ANN) are then trained on these features to predict the fractional chaotic system parameters. A fractional chaotic oscillator model is used through this work to demonstrate the developed technique. Numerical results show that recurrent Jordan-Elman neural networks with features obtained by the PSD estimate via Welch functions give adequate identification accuracy compared to other techniques.
Secure communication by generalized chaotic synchronization
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Chaotic communication is a rather new and active field of research. Although it is expected to have promising advantages,some investigators provide evidences that chaotic communication is not safety. This letter provides a new chaotic secure communi-cation scheme based on a generalized synchronization theory of coupled system. The secret message hidden in the chaotic sourcesignal generated via the scheme is very difficult to be unmasked by so-called nonlinear dynamic forecasting technique. One examplefor Internet communications was presented to illustrate the security of our scheme.
TOWARDS THRESHOLD FREQUENCY IN CHAOTIC COLPITTS OSCILLATOR
DEFF Research Database (Denmark)
Lindberg, Erik; Tamasevicius, Arunas; Mykolaitis, Gytis
2007-01-01
A novel version of chaotic Colpitts oscillator is described. Instead of a linear loss resistor, it includes an extra inductor and diode in the collector circuit of the transistor. The modified circuit in comparison with the common Colpitts oscillator may generate chaotic oscillations at the funda......A novel version of chaotic Colpitts oscillator is described. Instead of a linear loss resistor, it includes an extra inductor and diode in the collector circuit of the transistor. The modified circuit in comparison with the common Colpitts oscillator may generate chaotic oscillations...
Periodic and Chaotic Flapping of Insectile Wings
Huang, Yangyang
2015-01-01
Insects use flight muscles attached at the base of the wings to produce impressive wing flapping frequencies. The maximum power output of these flight muscles is insufficient to maintain such wing oscillations unless there is good elastic storage of energy in the insect flight system. Here, we explore the intrinsic self-oscillatory behavior of an insectile wing model, consisting of two rigid wings connected at their base by an elastic torsional spring. We study the wings behavior as a function of the total energy and spring stiffness. Three types of behavior are identified: end-over-end rotation, chaotic motion, and periodic flapping. Interestingly, the region of periodic flapping decreases as energy increases but is favored as stiffness increases. These findings are consistent with the fact that insect wings and flight muscles are stiff. They further imply that, by adjusting their muscle stiffness to the desired energy level, insects can maintain periodic flapping mechanically for a range of operating condit...
Foundations of chaotic mixing.
Wiggins, Stephen; Ottino, Julio M
2004-05-15
The simplest mixing problem corresponds to the mixing of a fluid with itself; this case provides a foundation on which the subject rests. The objective here is to study mixing independently of the mechanisms used to create the motion and review elements of theory focusing mostly on mathematical foundations and minimal models. The flows under consideration will be of two types: two-dimensional (2D) 'blinking flows', or three-dimensional (3D) duct flows. Given that mixing in continuous 3D duct flows depends critically on cross-sectional mixing, and that many microfluidic applications involve continuous flows, we focus on the essential aspects of mixing in 2D flows, as they provide a foundation from which to base our understanding of more complex cases. The baker's transformation is taken as the centrepiece for describing the dynamical systems framework. In particular, a hierarchy of characterizations of mixing exist, Bernoulli --> mixing --> ergodic, ordered according to the quality of mixing (the strongest first). Most importantly for the design process, we show how the so-called linked twist maps function as a minimal picture of mixing, provide a mathematical structure for understanding the type of 2D flows that arise in many micromixers already built, and give conditions guaranteeing the best quality mixing. Extensions of these concepts lead to first-principle-based designs without resorting to lengthy computations.
A NEW ONE-DIMENSIONAL CHAOTIC MAP WITH INFINITE COLLAPSES
Institute of Scientific and Technical Information of China (English)
Qiu Yuehong; He Chen; Zhu Hongwen
2002-01-01
This letter presents a new one-dimensional chaotic map with infinite collapses. Theoretical analyses show that the map has complicated dynamical behavior and ideal distribution.The map can be applied in chaotic spreading spectrum communication and chaotic cipher.
Complete and generalized synchronization in a class of noise perturbed chaotic systems
Chen, Zhang; Lin, Wei; Zhou, Jie
2007-06-01
In the paper, in light of the LaSalle-type invariance principle for stochastic differential equations, chaos synchronization is investigated for a class of chaotic systems dissatisfying a globally Lipschitz condition with noise perturbation. Sufficient criteria for both complete synchronization and generalized synchronization are rigorously established and thus successfully applied to realize chaos synchronization in the coupled unified chaotic systems. Furthermore, concrete examples as well as their numerical simulations are provided to illustrate the possible application of the established criteria.
Further results on complete synchronization for noise-perturbed chaotic systems
Zhou, Jie; Chen, Zhang
2008-08-01
In this Letter, a class of general systems which covers several famous chaotic systems is studied in complete synchronization with noise perturbation. Special nonlinear coupling techniques as well as LaSalle-type invariance principle of stochastic differential equations are employed to deduce our sufficient conditions for complete synchronization without involving the boundedness of chaotic systems. Furthermore, the correlative numerical simulations are given to illustrate the effectiveness of our theoretic results.
Further results on complete synchronization for noise-perturbed chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Zhou Jie [Research Center and Laboratory of Mathematics for Nonlinear Science, School of Mathematical Sciences, Fudan University, Shanghai 200433 (China)], E-mail: 031018020@fudan.edu.cn; Chen Zhang [School of Mathematics, Shandong University, Jinan 250100 (China)], E-mail: chenzhangcz@163.com
2008-08-11
In this Letter, a class of general systems which covers several famous chaotic systems is studied in complete synchronization with noise perturbation. Special nonlinear coupling techniques as well as LaSalle-type invariance principle of stochastic differential equations are employed to deduce our sufficient conditions for complete synchronization without involving the boundedness of chaotic systems. Furthermore, the correlative numerical simulations are given to illustrate the effectiveness of our theoretic results.
Chaos synchronization of fractional chaotic maps based on the stability condition
Wu, Guo-Cheng; Baleanu, Dumitru; Xie, He-Ping; Chen, Fu-Lai
2016-10-01
In the fractional calculus, one of the main challenges is to find suitable models which are properly described by discrete derivatives with memory. Fractional Logistic map and fractional Lorenz maps of Riemann-Liouville type are proposed in this paper. The general chaotic behaviors are investigated in comparison with the Caputo one. Chaos synchronization is designed according to the stability results. The numerical results show the method's effectiveness and fractional chaotic map's potential role for secure communication.
An Audio Data Encryption with Single and Double Dimension Discrete-Time Chaotic Systems
AKGÜL, Akif; KAÇAR, Sezgin; Pehlivan, İhsan
2015-01-01
— In this article, a study on increasing security of audio data encryption with single and double dimension discrete-time chaotic systems was carried out and application and security analyses were executed. Audio data samples of both mono and stereo types were encrypted. In the application here, single and double dimension discrete-time chaotic systems were used. In order to enhance security during encryption, a different method was applied by also using a non-linear function. In the chaos ba...
Chaotic Patterns in Aeroelastic Signals
Directory of Open Access Journals (Sweden)
F. D. Marques
2009-01-01
patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.
Anatomy of quantum chaotic eigenstates
Nonnenmacher, Stéphane
2010-01-01
The eigenfunctions of quantized chaotic systems cannot be described by explicit formulas, even approximate ones. This survey summarizes (selected) analytical approaches used to describe these eigenstates, in the semiclassical limit. The levels of description are macroscopic (one wants to understand the quantum averages of smooth observables), and microscopic (one wants informations on maxima of eigenfunctions, "scars" of periodic orbits, structure of the nodal sets and domains, local correlations), and often focusses on statistical results. Various models of "random wavefunctions" have been introduced to understand these statistical properties, with usually good agreement with the numerical data. We also discuss some specific systems (like arithmetic ones) which depart from these random models.
Chaotic behavior in dopamine neurodynamics.
King, R; Barchas, J D; Huberman, B A
1984-02-01
We report the results of the dynamics of a model of the central dopaminergic neuronal system. In particular, for certain values of a parameter k, which monitors the efficacy of dopamine at the postsynaptic receptor, chaotic solutions of the dynamical equations appear--a prediction that correlates with the observed increased variability in behavior among schizophrenics, the rapid fluctuations in motor activity among Parkinsonian patients treated chronically with L-dopa, and the lability of mood in some patients with an affective disorder. Moreover our hypothesis offers specific results concerning the appearance or disappearance of erratic solutions as a function of k and the external input to the dopamine neuronal system.
Wavelet filtering of chaotic data
Directory of Open Access Journals (Sweden)
M. Grzesiak
2000-01-01
Full Text Available Satisfactory method of removing noise from experimental chaotic data is still an open problem. Normally it is necessary to assume certain properties of the noise and dynamics, which one wants to extract, from time series. The wavelet based method of denoising of time series originating from low-dimensional dynamical systems and polluted by the Gaussian white noise is considered. Its efficiency is investigated by comparing the correlation dimension of clean and noisy data generated for some well-known dynamical systems. The wavelet method is contrasted with the singular value decomposition (SVD and finite impulse response (FIR filter methods.
Wavelet filtering of chaotic data
Grzesiak, M.
Satisfactory method of removing noise from experimental chaotic data is still an open problem. Normally it is necessary to assume certain properties of the noise and dynamics, which one wants to extract, from time series. The wavelet based method of denoising of time series originating from low-dimensional dynamical systems and polluted by the Gaussian white noise is considered. Its efficiency is investigated by comparing the correlation dimension of clean and noisy data generated for some well-known dynamical systems. The wavelet method is contrasted with the singular value decomposition (SVD) and finite impulse response (FIR) filter methods.
Cryptography Using Multiple Two-Dimensional Chaotic Maps
Directory of Open Access Journals (Sweden)
Ibrahim S. I. Abuhaiba
2012-08-01
Full Text Available In this paper, a symmetric key block cipher cryptosystem is proposed, involving multiple two-dimensional chaotic maps and using 128-bits external secret key. Computer simulations indicate that the cipher has good diffusion and confusion properties with respect to the plaintext and the key. Moreover, it produces ciphertext with random distribution. The computation time is much less than previous related works. Theoretic analysis verifies its superiority to previous cryptosystems against different types of attacks.
Theory and practice of chaotic cryptography
Energy Technology Data Exchange (ETDEWEB)
Amigo, J.M. [Centro de Investigacion Operativa, Universidad Miguel Hernandez, Avda. de la Universidad, 03202 Elche (Spain)]. E-mail: jm.amigo@umh.es; Kocarev, L. [Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0402 (United States)]. E-mail: lkocarev@ucsd.edu; Szczepanski, J. [Institute of Fundamental Technological Research, Polish Academy of Science, Swietokrzyska 21, 00-049 Warsaw (Poland)]. E-mail: jszczepa@ippt.gov.pl
2007-06-25
In this Letter we address some basic questions about chaotic cryptography, not least the very definition of chaos in discrete systems. We propose a conceptual framework and illustrate it with different examples from private and public key cryptography. We elaborate also on possible limits of chaotic cryptography.
Nonlinear chaotic model for predicting storm surges
Siek, M.; Solomatine, D.P.
This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables.
Is Navier-Stokes turbulence chaotic?
Deissler, R. G.
1986-01-01
Whether turbulent solutions of the Navier-Stokes equations are chaotic is considered. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions separate exponentially with time, having a positive Liapunov characteristic exponent. Thus the turbulence is characterized as chaotic.
Control of the chaotic driven pendulum
Baker, Gregory L.
1995-09-01
A method of controlling chaos (due to Ott, Grebogi, and Yorke) is illustrated with a simulated chaotic pendulum. The method consists of stabilizing a previously unstable periodic orbit through a feedback mechanism that periodically adjusts the damping parameter of the pendulum. The presentation is pedagogical and describes the method in more detail than is typical of the research literature on controlling chaotic systems.
Chaotic coupling synchronization of hyperchaotic oscillators
Institute of Scientific and Technical Information of China (English)
Zou Yan-Li; Zhu Jie; Chen Guan-Rong
2005-01-01
In this paper, two kinds of chaotic coupling synchronization schemes are presented. The synchronizability of the coupled hyperchaotic oscillators is proved mathematically and the numerical simulation is also carried out. The numerical calculation of the largest conditional Lyapunov exponent shows that in a given range of coupling strengths,chaotic-coupling synchronization is quicker than the typical continuous-coupling synchronization.
Application of chaotic theory to parameter estimation
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
High precision parameter estimation is very important for control system design and compensation. This paper utilizes the properties of chaotic system for parameter estimation. Theoretical analysis and experimental results indicated that this method has extremely high sensitivity and resolving power. The most important contribution of this paper is apart from the traditional engineering viewpoint and actualizing parameter estimation just based on unstable chaotic systems.
Chaotic Hypothesis and Universal Large Deviations Properties
Gallavotti, G
1998-01-01
Chaotic systems arise naturally in Statistical Mechanics and in Fluid Dynamics. A paradigm for their modelization are smooth hyperbolic systems. Are there consequences that can be drawn simply by assuming that a system is hyperbolic? here we present a few model independent general consequences which may have some relevance for the Physics of chaotic systems. Expanded version of a talk at ICM98, Berlin.
Fuzzy Modeling, Tracking Control and Synchronization of the Rossler's Chaotic System
Institute of Scientific and Technical Information of China (English)
方建安; 范丹丹
2004-01-01
In this paper, a novel method to model, track control and synchronize the Rossler's chaotic system is proposed. The fuzzy logical system is used so that the fuzzy inference rule is transferred into a type of variable coef ficient nonlinear ordinary differential equation. Consequently the model of the chaotic system is obtained. Then a fuzzy tracking control and a fuzzy synchronization for chaotic systems is proposed as well. First, a known tracking control for the Rossler's system is used in this paper. We represent the Rossler's chaotic and control systems into fuzzy inference rules. Then the variable coefficient nonlinear ordinary differential equation is also got. Simulation results show that such an approach is effective and has a high precision.
Synchronisation of chaotic systems using a novel sampled-data fuzzy controller
Institute of Scientific and Technical Information of China (English)
Feng Yi-Fu; Zhang Qing-Ling
2011-01-01
This paper presents the synchronisation of chaotic systems using a sampled-data fuzzy controller and is meaningful for many physical real-life applications. Firstly, a Takagi-Sugeno (T-S) fuzzy model is employed to represent the chaotic systems that contain some nonlinear terms, then a type of fuzzy sampled-data controller is proposed and an error system formed by the response and drive chaotic system. Secondly, relaxed LMI-based synchronisation conditions are derived by using a new paraneter-dependent Lyapunov-Krasovskii functional and relaxed stabilisation techniques for the underlying error system. The derived LMI-based conditions are used to aid the design of a sampled-data fuzzy controller to achieve the synchronisation of chaotic systems. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.
A Hybrid Chaotic Quantum Evolutionary Algorithm
DEFF Research Database (Denmark)
Cai, Y.; Zhang, M.; Cai, H.
2010-01-01
A hybrid chaotic quantum evolutionary algorithm is proposed to reduce amount of computation, speed up convergence and restrain premature phenomena of quantum evolutionary algorithm. The proposed algorithm adopts the chaotic initialization method to generate initial population which will form...... and enhance the global search ability. A large number of tests show that the proposed algorithm has higher convergence speed and better optimizing ability than quantum evolutionary algorithm, real-coded quantum evolutionary algorithm and hybrid quantum genetic algorithm. Tests also show that when chaos...... is introduced to quantum evolutionary algorithm, the hybrid chaotic search strategy is superior to the carrier chaotic strategy, and has better comprehensive performance than the chaotic mutation strategy in most of cases. Especially, the proposed algorithm is the only one that has 100% convergence rate in all...
Simple driven chaotic oscillators with complex variables.
Marshall, Delmar; Sprott, J C
2009-03-01
Despite a search, no chaotic driven complex-variable oscillators of the form z+f(z)=e(iOmegat) or z+f(z)=e(iOmegat) are found, where f is a polynomial with real coefficients. It is shown that, for analytic functions f(z), driven complex-variable oscillators of the form z+f(z)=e(iOmegat) cannot have chaotic solutions. Seven simple driven chaotic oscillators of the form z+f(z,z)=e(iOmegat) with polynomial f(z,z) are given. Their chaotic attractors are displayed, and Lyapunov spectra are calculated. Attractors for two of the cases have symmetry across the x=-y line. The systems' behavior with Omega as a control parameter in the range of Omega=0.1-2.0 is examined, revealing cases of period doubling, intermittency, chaotic transients, and period adding as routes to chaos. Numerous cases of coexisting attractors are also observed.
Trend prediction of chaotic time series
Institute of Scientific and Technical Information of China (English)
Li Aiguo; Zhao Cai; Li Zhanhuai
2007-01-01
To predict the trend of chaotic time series in time series analysis and time series data mining fields, a novel predicting algorithm of chaotic time series trend is presented, and an on-line segmenting algorithm is proposed to convert a time series into a binary string according to ascending or descending trend of each subsequence. The on-line segmenting algorithm is independent of the prior knowledge about time series. The naive Bayesian algorithm is then employed to predict the trend of chaotic time series according to the binary string. The experimental results of three chaotic time series demonstrate that the proposed method predicts the ascending or descending trend of chaotic time series with few error.
Chaotic Motion of Corrugated Circular Plates
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Large deflection theory of thin anisotropic circular plates was used to analyze the bifurcation behavior and chaotic phenomena of a corrugated thin circular plate with combined transverse periodic excitation and an in-plane static boundary load. The nonlinear dynamic equation for the corrugated plate was derived by employing Galerkin's technique. The critical conditions for occurrence of the homoclinic and subharmonic bifurcations as well as chaos were studied theoretically using the Melnikov function method. The chaotic motion was also simulated numerically using Maple, with the Poincaré map and phase curve used to evaluate when chaotic motion appears. The results indicate some chaotic motion in the corrugated plate. The method is directly applicable to chaotic analysis of an isotropic circular plate.
Chaotic control and synchronization for system identification.
Carroll, T L
2004-04-01
Research into applications of synchronized chaotic systems assumes that it will be necessary to build many different drive-response pairs, but little is known in general about designing higher dimensional chaotic flows. In this paper, I do not add any design techniques, but I show that it is possible to create multiple drive-response pairs from one chaotic system by applying chaos control techniques to the drive and response systems. If one can design one chaotic system with the desired properties, then many drive-response pairs can be built from this system, so that it is not necessary to solve the design problem more than once. I show both numerical simulations and experimental work with chaotic circuits. I also test the response systems for ability to overcome noise or other interference.
Energy Technology Data Exchange (ETDEWEB)
Enqvist, Kari [Physics Department, University of Helsinki, and Helsinki Institute of Physics, FIN-00014 Helsinki (Finland); Koivisto, Tomi [Institute for Theoretical Physics and Spinoza Institute, Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Rigopoulos, Gerasimos, E-mail: kari.enqvist@helsinki.fi, E-mail: T.S.Koivisto@astro.uio.no, E-mail: rigopoulos@physik.rwth-aachen.de [Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, D-52056 Aachen (Germany)
2012-05-01
We consider inflation within the context of what is arguably the simplest non-metric extension of Einstein gravity. There non-metricity is described by a single graviscalar field with a non-minimal kinetic coupling to the inflaton field Ψ, parameterized by a single parameter γ. There is a simple equivalent description in terms of a massless field and an inflaton with a modified potential. We discuss the implications of non-metricity for chaotic inflation and find that it significantly alters the inflaton dynamics for field values Ψ∼>M{sub P}/γ, dramatically changing the qualitative behaviour in this regime. In the equivalent single-field description this is described as a cuspy potential that forms of barrier beyond which the inflation becomes a ghost field. This imposes an upper bound on the possible number of e-folds. For the simplest chaotic inflation models, the spectral index and the tensor-to-scalar ratio receive small corrections dependent on the non-metricity parameter. We also argue that significant post-inflationary non-metricity may be generated.
Robust dynamical effects in traffic and chaotic maps on trees
Indian Academy of Sciences (India)
Bosiljka Tadić; Zoran Levnajić
2008-06-01
In the dynamic processes on networks collective effects emerge due to the couplings between nodes, where the network structure may play an important role. Interaction along many network links in the nonlinear dynamics may lead to a kind of chaotic collective behavior. Here we study two types of well-defined diffusive dynamics on scale-free trees: traffic of packets as navigated random walks, and chaotic standard maps coupled along the network links. We show that in both cases robust collective dynamic effects appear, which can be measured statistically and related to non-ergodicity of the dynamics on the network. Specifically, we find universal features in the fluctuations of time series and appropriately defined return-time statistics.
Chaotic time series. Part II. System Identification and Prediction
Directory of Open Access Journals (Sweden)
Bjørn Lillekjendlie
1994-10-01
Full Text Available This paper is the second in a series of two, and describes the current state of the art in modeling and prediction of chaotic time series. Sample data from deterministic non-linear systems may look stochastic when analysed with linear methods. However, the deterministic structure may be uncovered and non-linear models constructed that allow improved prediction. We give the background for such methods from a geometrical point of view, and briefly describe the following types of methods: global polynomials, local polynomials, multilayer perceptrons and semi-local methods including radial basis functions. Some illustrative examples from known chaotic systems are presented, emphasising the increase in prediction error with time. We compare some of the algorithms with respect to prediction accuracy and storage requirements, and list applications of these methods to real data from widely different areas.
Chaotic time series; 2, system identification and prediction
Lillekjendlie, B
1994-01-01
This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear methods. However, the deterministic structure may be uncovered and non-linear models constructed that allow improved prediction. We give the background for such methods from a geometrical point of view, and briefly describe the following types of methods: global polynomials, local polynomials, multi layer perceptrons and semi-local methods including radial basis functions. Some illustrative examples from known chaotic systems are presented, emphasising the increase in prediction error with time. We compare some of the algorithms with respect to prediction accuracy and storage requirements, and list applications of these methods to real data from widely different areas.
Robust adaptive synchronization of chaotic neural networks by slide technique
Institute of Scientific and Technical Information of China (English)
Lou Xu-Yang; Cui Bao-Tong
2008-01-01
In this paper,we focus on the robust adaptive synchronization between two coupled chaotic neural networks with all the parameters unknown and time-varying delay.In order to increase the robustness of the two coupled neural networks,the key idea is that a sliding-mode-type controller is employed.Moreover,without the estimate values of the network unknown parameters taken as an updating object,a new updating object is introduced in the constructing of controller.Using the proposed controller,without any requirements for the boundedness,monotonicity and differentiability of activation functions,and symmetry of connections,the two coupled chaotic neural networks can achieve global robust synchronization no matter what their initial states are.Finally,the numerical simulation validates the effectiveness and feasibility of the proposed technique.
Spread-spectrum communication using binary spatiotemporal chaotic codes
Wang, Xingang; Zhan, Meng; Gong, Xiaofeng; Lai, Choy Heng; Lai, Ying-Cheng
2005-01-01
We propose a scheme to generate binary code for baseband spread-spectrum communication by using a chain of coupled chaotic maps. We compare the performances of this type of spatiotemporal chaotic code with those of a conventional code used frequently in digital communication, the Gold code, and demonstrate that our code is comparable or even superior to the Gold code in several key aspects: security, bit error rate, code generation speed, and the number of possible code sequences. As the field of communicating with chaos faces doubts in terms of performance comparison with conventional digital communication schemes, our work gives a clear message that communicating with chaos can be advantageous and it deserves further attention from the nonlinear science community.
Chaotic dynamics of flexible Euler-Bernoulli beams.
Awrejcewicz, J; Krysko, A V; Kutepov, I E; Zagniboroda, N A; Dobriyan, V; Krysko, V A
2013-12-01
Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c(2)) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q(0) and frequency ω(p) of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.
Fuzzy modeling and synchronization of hyper chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Zhang Hongbin [Center for Nonlinear and Complex Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)] e-mail: zhanghb@uestc.edu.cn; Liao Xiaofeng [Center for Nonlinear and Complex Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China); Institute of Computer Science, Chongqing University, Chongqing 400044 (China); Yu Juebang [Center for Nonlinear and Complex Systems, School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)
2005-11-01
This paper presents fuzzy model-based designs for synchronization of hyper chaotic systems. The T-S fuzzy models for hyper chaotic systems are exactly derived. Based on the T-S fuzzy hyper chaotic models, the fuzzy controllers for hyper chaotic synchronization are designed via the exact linearization techniques. Numerical examples are given to demonstrate the effectiveness of the proposed method.
CHAOTIC CONTROL OF NONLINEAR SYSTEMS BASED ON IMPROVED CORRELATIVITY
Institute of Scientific and Technical Information of China (English)
Zhou Xiaoan; Zhang Jihong
2003-01-01
Chaotic sequences are basically ergodic random sequences. By improving correlativity of a chaotic signal, the chaotic dynamic system can be controlled to converge to its equilibrium point and, more significantly, to its multi-periodic orbits. Mathematical theory analysis is carried out and some computer simulation results are provided to support such controllability of the chaotic Henon system and the discrete coupled map lattice.
Multiple channel secure communication using chaotic system encoding
Energy Technology Data Exchange (ETDEWEB)
Miller, S.L.
1996-12-31
fA new method to encrypt signals using chaotic systems has been developed that offers benefits over conventional chaotic encryption methods. The method simultaneously encodes multiple plaintext streams using a chaotic system; a key is required to extract the plaintext from the chaotic cipertext. A working prototype demonstrates feasibility of the method by simultaneously encoding and decoding multiple audio signals using electrical circuits.
Threshold control of chaotic neural network.
He, Guoguang; Shrimali, Manish Dev; Aihara, Kazuyuki
2008-01-01
The chaotic neural network constructed with chaotic neurons exhibits rich dynamic behaviour with a nonperiodic associative memory. In the chaotic neural network, however, it is difficult to distinguish the stored patterns in the output patterns because of the chaotic state of the network. In order to apply the nonperiodic associative memory into information search, pattern recognition etc. it is necessary to control chaos in the chaotic neural network. We have studied the chaotic neural network with threshold activated coupling, which provides a controlled network with associative memory dynamics. The network converges to one of its stored patterns or/and reverse patterns which has the smallest Hamming distance from the initial state of the network. The range of the threshold applied to control the neurons in the network depends on the noise level in the initial pattern and decreases with the increase of noise. The chaos control in the chaotic neural network by threshold activated coupling at varying time interval provides controlled output patterns with different temporal periods which depend upon the control parameters.
Behavioural analysis of a time series–A chaotic approach
Indian Academy of Sciences (India)
T A Fathima; V Jothiprakash
2014-06-01
Out of the various methods available to study the chaotic behaviour, correlation dimension method (CDM) derived from Grassberger-Procaccia algorithm and False Nearest Neighbour method (FNN) are widely used. It is aimed to study the adaptability of those techniques for Indian rainfall data that is dominated by monsoon. In the present study, five sets of time series data are analyzed using correlation dimension method (CDM) based upon Grassberger-Procaccia algorithm for studying their behaviour. In order to confirm the results arrived from correlation dimension method, FNN and phase randomisation method is also applied to the time series used in the present study to fix the optimum embedding dimension. First series is a deterministic natural number series, the next two series are random number series with two types of distributions; one is uniform and another is normal distributed random number series. The fourth series is Henon data, an erratic data generated from a deterministic non linear equation (classified as chaotic series). After checking the applicability of correlation dimension method for deterministic, stochastic and chaotic data (known series) the method is applied to a rainfall time series observed at Koyna station, Maharashtra, India for its behavioural study. The results obtained from the chaotic analysis revealed that CDM is an efficient method for behavioural study of a time series. It also provides first hand information on the number of dimensions to be considered for time series prediction modelling. The CDM applied to real life rainfall data brings out the nature of rainfall at Koyna station as chaotic. For the rainfall data, CDM resulted in a minimum correlation dimension of one and optimum dimension as five. FNN method also resulted in five dimensions for the rainfall data. The behaviour of the rainfall time series is further confirmed by phase randomisation technique also. The surrogate data derived from randomisation gives entirely different
Urey Prize Lecture - Chaotic dynamics in the solar system
Wisdom, Jack
1987-01-01
Attention is given to solar system cases in which chaotic solutions of Newton's equations are important, as in chaotic rotation and orbital evolution. Hyperion is noted to be tumbling chaotically; chaotic orbital evolution is suggested to be of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean-motion commensurability with Jupiter. In addition, chaotic trajectories in the 2/1 chaotic zone reach very high eccentricities by a route that carries them to high inclinations temporarily.
SPECIAL DYNAMIC BEHAVIORS OF A TEMPORAL CHAOTIC SYSTEM
Institute of Scientific and Technical Information of China (English)
Mingxuan Zhang; Jinjiang Yu; Wangqiang Han
2008-01-01
When dynamic behaviors of temporal chaotic system are analyzed,we find that a temporal chaotic system has not only genetic dynamic behaviors of chaotic reflection,but also has phenomena influencing two chaotic attractors by original values.Along with the system parameters changing to certain value,the system will appear a break in chaotic region,and jump to another orbit of attractors.When it is opposite that the system parameters change direction,the temporal chaotic system appears complicated chaotic behaviors.
Chaotic neurodynamics for autonomous agents.
Harter, Derek; Kozma, Robert
2005-05-01
Mesoscopic level neurodynamics study the collective dynamical behavior of neural populations. Such models are becoming increasingly important in understanding large-scale brain processes. Brains exhibit aperiodic oscillations with a much more rich dynamical behavior than fixed-point and limit-cycle approximation allow. Here we present a discretized model inspired by Freeman's K-set mesoscopic level population model. We show that this version is capable of replicating the important principles of aperiodic/chaotic neurodynamics while being fast enough for use in real-time autonomous agent applications. This simplification of the K model provides many advantages not only in terms of efficiency but in simplicity and its ability to be analyzed in terms of its dynamical properties. We study the discrete version using a multilayer, highly recurrent model of the neural architecture of perceptual brain areas. We use this architecture to develop example action selection mechanisms in an autonomous agent.
Chaotic behaviour in speculative markets
Directory of Open Access Journals (Sweden)
García Artiles, María Dolores
2001-01-01
Full Text Available An asset price model of speculative financial market with fundamentalists and chartists is analyzed. Our model explains bursts of volatility in financial markets, which are not well explained by the traditional finance paradigms, as we will show. Depending on the time lag in the formation of chartists' expectations, the system evolves through several dynamic regimes finishing in a strange attractor. Chaos provides a self-sustained motion around the rationally expected equilibrium that corresponds to a speculative bubble. In order to explain the role of Chartism, chaotic motion is a very interesting theoretical feature for a speculative financial market model. It provides a complex non-linear dynamic behaviour around the Walrasian equilibrium price produced by deterministic interactions between fundamentalists and chartists
Chaotic dynamics of propeller singing
Institute of Scientific and Technical Information of China (English)
YU Dapeng; ZHAO Deyou; WANG Yu
2012-01-01
The system of propeller singing is proved for the first time to have the character of chaotic dynamics through the study of the signal time series. The estimation of the topolog- ical dimension, the confirmation of the number of independent variable and the description of the character of attractor trajectory in reconstructed phase space are implemented during the analysis of the system. The result indicates that the system of propeller singing can be recon- structed by the optional delay time tD = 1, the minimal embedding dimension dE = 8, and the reconstructed topological parameter with the fractional correlation dimension D2 = 5.1579 and the positive maximum Lyapunov exponent λtD=0.0771. The results provide a new approach to the further study of the propeller singing phenomenon.
Chaotic renormalization-group trajectories
DEFF Research Database (Denmark)
Damgaard, Poul H.; Thorleifsson, G.
1991-01-01
, or in regions where the renormalization-group flow becomes chaotic. We present some explicit examples of these phenomena for the case of a Lie group valued spin-model analyzed by means of a variational real-space renormalization group. By directly computing the free energy of these models around the parameter......Under certain conditions, the renormalization-group flow of models in statistical mechanics can change dramatically under just very small changes of given external parameters. This can typically occur close to bifurcations of fixed points, close to the complete disappearance of fixed points...... regions in which such nontrivial modifications of the renormalization-group flow occur, we can extract the physical consequences of these phenomena....
Gaussian fluctuations in chaotic eigenstates
Srednicki, M A; Srednicki, Mark; Stiernelof, Frank
1996-01-01
We study the fluctuations that are predicted in the autocorrelation function of an energy eigenstate of a chaotic, two-dimensional billiard by the conjecture (due to Berry) that the eigenfunction is a gaussian random variable. We find an explicit formula for the root-mean-square amplitude of the expected fluctuations in the autocorrelation function. These fluctuations turn out to be O(\\hbar^{1/2}) in the small \\hbar (high energy) limit. For comparison, any corrections due to scars from isolated periodic orbits would also be O(\\hbar^{1/2}). The fluctuations take on a particularly simple form if the autocorrelation function is averaged over the direction of the separation vector. We compare our various predictions with recent numerical computations of Li and Robnik for the Robnik billiard, and find good agreement. We indicate how our results generalize to higher dimensions.
Chaotic eigenfunctions in momentum space
Bäcker, A; Bäcker, Arnd; Schubert, Roman
1999-01-01
We study eigenstates of chaotic billiards in the momentum representation and propose the radially integrated momentum distribution as useful measure to detect localization effects. For the momentum distribution, the radially integrated momentum distribution, and the angular integrated momentum distribution explicit formulae in terms of the normal derivative along the billiard boundary are derived. We present a detailed numerical study for the stadium and the cardioid billiard, which shows in several cases that the radially integrated momentum distribution is a good indicator of localized eigenstates, such as scars, or bouncing ball modes. We also find examples, where the localization is more strongly pronounced in position space than in momentum space, which we discuss in detail. Finally applications and generalizations are discussed.
Output Regulation of the Arneodo Chaotic System
Directory of Open Access Journals (Sweden)
Sundarapandian Vaidyanathan
2010-08-01
Full Text Available This paper solves the problem of regulating the output of the Arneodo chaotic system (1981, which is one of the paradigms of chaotic dynamical systems. Explicitly, using the state feedback control laws, the output of the Arneodo chaotic system is regulated so as to track constant reference signals as well as to track periodic reference signals. The control laws are derived using the regulator equations of Byrnes and Isidori (1990, which provide the solution of the output regulation problem for nonlinear control systems involving neutrally stable exosystem dynamics. Numerical results are shown to verify the results.
Polynomial chaotic inflation in supergravity revisited
Directory of Open Access Journals (Sweden)
Kazunori Nakayama
2014-10-01
Full Text Available We revisit a polynomial chaotic inflation model in supergravity which we proposed soon after the Planck first data release. Recently some issues have been raised in Ref. [12], concerning the validity of our polynomial chaotic inflation model. We study the inflaton dynamics in detail, and confirm that the inflaton potential is very well approximated by a polynomial potential for the parameters of our interest in any practical sense, and in particular, the spectral index and the tensor-to-scalar ratio can be estimated by single-field approximation. This justifies our analysis of the polynomial chaotic inflation in supergravity.
Improving the prediction of chaotic time series
Institute of Scientific and Technical Information of China (English)
李克平; 高自友; 陈天仑
2003-01-01
One of the features of deterministic chaos is sensitive to initial conditions. This feature limits the prediction horizons of many chaotic systems. In this paper, we propose a new prediction technique for chaotic time series. In our method, some neighbouring points of the predicted point, for which the corresponding local Lyapunov exponent is particularly large, would be discarded during estimating the local dynamics, and thus the error accumulated by the prediction algorithm is reduced. The model is tested for the convection amplitude of Lorenz systems. The simulation results indicate that the prediction technique can improve the prediction of chaotic time series.
Synchronization of Time-Continuous Chaotic Oscillators
DEFF Research Database (Denmark)
Yanchuk, S.; Maistrenko, Yuri; Mosekilde, Erik
2003-01-01
Considering a system of two coupled identical chaotic oscillators, the paper first establishes the conditions of transverse stability for the fully synchronized chaotic state. Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded...... the interacting chaotic oscillators causes a shift of the synchronization manifold. The presence of a coupling asymmetry is found to lead to further modifications of the destabilization process. Finally, the paper considers the problem of partial synchronization in a system of four coupled Rossler oscillators...
Synchronization Techniques for Chaotic Communication Systems
Jovic, Branislav
2011-01-01
Since the early 1990s, when synchronization of chaotic communication systems became a popular research subject, a vast number of scientific papers have been published. However, most of today's books on chaotic communication systems deal exclusively with the systems where perfect synchronization is assumed, an assumption which separates theoretical from practical, real world, systems. This book is the first of its kind dealing exclusively with the synchronization techniques for chaotic communication systems. It describes a number of novel robust synchronization techniques, which there is a lack
Chaotic ant swarm optimization to economic dispatch
Energy Technology Data Exchange (ETDEWEB)
Cai, Jiejin; Ma, Xiaoqian [Electric Power College, South China University of Technology, Guangzhou 510640 (China); Li, Lixiang; Yang, Yixian [Information Security Center, Department of Information Engineering, Beijing University of Posts and Telecommunications, Beijing 100876 (China); State Key Laboratory of Networking and Switching, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Peng, Haipeng [Information Security Center, Department of Information Engineering, Beijing University of Posts and Telecommunications, Beijing 100876 (China); State Key Laboratory of Networking and Switching, Beijing University of Posts and Telecommunications, Beijing 100876 (China); School of Information Science and Engineering, Shenyang University of Technology, Shenyang 110023 (China); Wang, Xiangdong [School of Information Science and Engineering, Shenyang University of Technology, Shenyang 110023 (China)
2007-08-15
This paper developed a novel algorithm named chaotic ant swarm optimization (CASO) for solving the economic dispatch (ED) problems of thermal generators in power systems. This algorithm combines with the chaotic and self-organization behavior of ants in the foraging process. It includes both effects of chaotic dynamics and swarm-based search. The algorithm was employed to solve the ED problems of thermal generators. The proposed method was applied to three examples of power systems. Simulation results demonstrated that the method can obtain feasible and effective solutions, and it is a promising alternative approach for solving the ED problems in practical power systems. (author)
Regular transport dynamics produce chaotic travel times.
Villalobos, Jorge; Muñoz, Víctor; Rogan, José; Zarama, Roberto; Johnson, Neil F; Toledo, Benjamín; Valdivia, Juan Alejandro
2014-06-01
In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system.
Chaotic mixer improves microarray hybridization.
McQuain, Mark K; Seale, Kevin; Peek, Joel; Fisher, Timothy S; Levy, Shawn; Stremler, Mark A; Haselton, Frederick R
2004-02-15
Hybridization is an important aspect of microarray experimental design which influences array signal levels and the repeatability of data within an array and across different arrays. Current methods typically require 24h and use target inefficiently. In these studies, we compare hybridization signals obtained in conventional static hybridization, which depends on diffusional target delivery, with signals obtained in a dynamic hybridization chamber, which employs a fluid mixer based on chaotic advection theory to deliver targets across a conventional glass slide array. Microarrays were printed with a pattern of 102 identical probe spots containing a 65-mer oligonucleotide capture probe. Hybridization of a 725-bp fluorescently labeled target was used to measure average target hybridization levels, local signal-to-noise ratios, and array hybridization uniformity. Dynamic hybridization for 1h with 1 or 10ng of target DNA increased hybridization signal intensities approximately threefold over a 24-h static hybridization. Similarly, a 10- or 60-min dynamic hybridization of 10ng of target DNA increased hybridization signal intensities fourfold over a 24h static hybridization. In time course studies, static hybridization reached a maximum within 8 to 12h using either 1 or 10ng of target. In time course studies using the dynamic hybridization chamber, hybridization using 1ng of target increased to a maximum at 4h and that using 10ng of target did not vary over the time points tested. In comparison to static hybridization, dynamic hybridization reduced the signal-to-noise ratios threefold and reduced spot-to-spot variation twofold. Therefore, we conclude that dynamic hybridization based on a chaotic mixer design improves both the speed of hybridization and the maximum level of hybridization while increasing signal-to-noise ratios and reducing spot-to-spot variation.
Directory of Open Access Journals (Sweden)
Jesus Manuel Munoz-Pacheco
2013-01-01
Full Text Available An algorithm to compute the Lyapunov exponents of piecewise linear function-based multidirectional multiscroll chaotic oscillators is reported. Based on the m regions in the piecewise linear functions, the suggested algorithm determines the individual expansion rate of Lyapunov exponents from m-piecewise linear variational equations and their associated m-Jacobian matrices whose entries remain constant during all computation cycles. Additionally, by considering OpAmp-based chaotic oscillators, we study the impact of two analog design procedures on the magnitude of Lyapunov exponents. We focus on analyzing variations of both frequency bandwidth and voltage/current dynamic range of the chaotic signals at electronic system level. As a function of the design parameters, a renormalization factor is proposed to estimate correctly the Lyapunov spectrum. Numerical simulation results in a double-scroll type chaotic oscillator and complex chaotic oscillators generating multidirectional multiscroll chaotic attractors on phase space confirm the usefulness of the reported algorithm.
Energy Technology Data Exchange (ETDEWEB)
Sabavath, Gopi Kishan; Banerjee, I.; Mahapatra, S. K., E-mail: skmahapatra@bitmesra.ac.in [Plasma Laboratory, Department of Physics, Birla Institute of Technology-Mesra, Ranchi 835215 (India); Shaw, Pankaj Kumar; Sekar Iyengar, A. N. [Plasma Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064 (India)
2015-08-15
Floating potential fluctuations from a direct current magnetron sputtering plasma have been analysed using time series analysis techniques like phase space plots, power spectra, frequency bifurcation plot, etc. The system exhibits quasiperiodic-chaotic-quasiperiodic-chaotic transitions as the discharge voltage was increased. The transitions of the fluctuations, quantified using the largest Lyapunov exponent, have been corroborated by Hurst exponent and the Shannon entropy. The Shannon entropy is high for quasiperiodic and low for chaotic oscillations.
Quantum localization of chaotic eigenstates and the level spacing distribution
Batistić, Benjamin; Robnik, Marko
2013-11-01
The phenomenon of quantum localization in classically chaotic eigenstates is one of the main issues in quantum chaos (or wave chaos), and thus plays an important role in general quantum mechanics or even in general wave mechanics. In this work we propose two different localization measures characterizing the degree of quantum localization, and study their relation to another fundamental aspect of quantum chaos, namely the (energy) spectral statistics. Our approach and method is quite general, and we apply it to billiard systems. One of the signatures of the localization of chaotic eigenstates is a fractional power-law repulsion between the nearest energy levels in the sense that the probability density to find successive levels on a distance S goes like ∝Sβ for small S, where 0≤β≤1, and β=1 corresponds to completely extended states. We show that there is a clear functional relation between the exponent β and the two different localization measures. One is based on the information entropy and the other one on the correlation properties of the Husimi functions. We show that the two definitions are surprisingly linearly equivalent. The approach is applied in the case of a mixed-type billiard system [M. Robnik, J. Phys. A: Math. Gen.JPHAC50305-447010.1088/0305-4470/16/17/014 16, 3971 (1983)], in which the separation of regular and chaotic eigenstates is performed.
Chaotic orbits of a pendulum with variable length
Directory of Open Access Journals (Sweden)
Massimo Furi
2004-03-01
Full Text Available The main purpose of this investigation is to show that a pendulum, whose pivot oscillates vertically in a periodic fashion, has uncountably many chaotic orbits. The attribute chaotic is given according to the criterion we now describe. First, we associate to any orbit a finite or infinite sequence as follows. We write 1 or $-1$ every time the pendulum crosses the position of unstable equilibrium with positive (counterclockwise or negative (clockwise velocity, respectively. We write 0 whenever we find a pair of consecutive zero's of the velocity separated only by a crossing of the stable equilibrium, and with the understanding that different pairs cannot share a common time of zero velocity. Finally, the symbol $omega$, that is used only as the ending symbol of a finite sequence, indicates that the orbit tends asymptotically to the position of unstable equilibrium. Every infinite sequence of the three symbols ${1,-1,0}$ represents a real number of the interval $[0,1]$ written in base 3 when $-1$ is replaced with 2. An orbit is considered chaotic whenever the associated sequence of the three symbols ${1,2,0}$ is an irrational number of $[0,1]$. Our main goal is to show that there are uncountably many orbits of this type.
Organizational Knowledge Conversion and Creation Processes in a Chaotic Environment
Directory of Open Access Journals (Sweden)
Andrei Ștefan NESTIAN
2013-05-01
Full Text Available This is an explorative and conceptual paper, based on the analysis and comparison of relevant literature. the purpose of the article is to clarify the differences between knowledge creating processes and knowledge conversion processes, by analysing them when confronted with a chaotic environment. the way the knowledge conversion and creation processes are presented by Ikujiro Nonaka and his co-workers suggests the necessary existence of a Ba in order to generate the spiral of knowledge creation. this implies the acceptance of a relationship between the environment and the knowledge conversion process, in which the environment influences the knowledge creation. the article is based on the hypothesis that a chaotic environment, characterized by unpredictability, non-linearity and crisis, will lead to specific ways of functioning of the knowledge creation and conversion process that highlight the relations between the two different types of processes. Starting from the general concept of resilience, herein one proposes and explains the concept of resilience of the knowledge conversion system. the role of the attractors from the chaotic environment in the creation of new knowledge is identified and explained
A chaotic system with only one stable equilibrium
Xiong, Wang
2011-01-01
If you are given a simple three-dimensional autonomous quadratic system that has only one stable equilibrium, what would you predict its dynamics to be, stable or periodic? Will it be surprising if you are shown that such a system is actually chaotic? Although chaos theory for three-dimensional autonomous systems has been intensively and extensively studied since the time of Lorenz in the 1960s, and the theory has become quite mature today, it seems that no one would anticipate a possibility of finding a three-dimensional autonomous quadratic chaotic system with only one stable equilibrium. The discovery of the new system, to be reported in this Letter, is indeed striking because for a three-dimensional autonomous quadratic system with a single stable node-focus equilibrium, one typically would anticipate non-chaotic and even asymptotically converging behaviors. Although the new system is not of saddle-focus type, therefore the familiar \\v{S}i'lnikov homoclinic criterion is not applicable, it is demonstrated ...
Encryption in Chaotic Systems with Sinusoidal Excitations
Directory of Open Access Journals (Sweden)
G. Obregón-Pulido
2014-01-01
Full Text Available In this contribution an encryption method using a chaotic oscillator, excited by “n” sinusoidal signals, is presented. The chaotic oscillator is excited by a sum of “n” sinusoidal signals and a message. The objective is to encrypt such a message using the chaotic behavior and transmit it, and, as the chaotic system is perturbed by the sinusoidal signal, the transmission security could be increased due to the effect of such a perturbation. The procedure is based on the regulation theory and consider that the receiver knows the frequencies of the perturbing signal, with this considerations the algorithm estimates the excitation in such a way that the receiver can cancel out the perturbation and all the undesirable dynamics in order to produce only the message. In this way we consider that the security level is increased.
Nonlinear chaotic model for predicting storm surges
Directory of Open Access Journals (Sweden)
M. Siek
2010-09-01
Full Text Available This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables. We implemented the univariate and multivariate chaotic models with direct and multi-steps prediction techniques and optimized these models using an exhaustive search method. The built models were tested for predicting storm surge dynamics for different stormy conditions in the North Sea, and are compared to neural network models. The results show that the chaotic models can generally provide reliable and accurate short-term storm surge predictions.
Adaptive tracking control of chaotic systems
Institute of Scientific and Technical Information of China (English)
卢钊; 卢和
2004-01-01
It is important to develop control techniques able to control not only known chaos but also chaotic systems with unknown parameters. This paper proposes a novel adaptive tracking control approach for identifying the unknown parameters and controlling the chaos, which is not closely related to the particular chaotic system to be controlled. The global uniform boundedness of estimated parameters and the asymptotical stability of the tracking errors are proved by Lyapunov stability theory and LaSalle-Yoshizawa theorem. The suggested method enables stabilization of chaotic motion to a steady state ad well as tracking of any desired trajectory to be achieved in a systematic way. Computer simulation on a complex chaotic system illustrtes the effectiveness of the proposed control method.
A concise guide to chaotic electronic circuits
Buscarino, Arturo; Frasca, Mattia; Sciuto, Gregorio
2014-01-01
This brief provides a source of instruction from which students can be taught about the practicalities of designing and using chaotic circuits. The text provides information on suitable materials, circuit design and schemes for design realization. Readers are then shown how to reproduce experiments on chaos and to design new ones. The text guides the reader easily from the basic idea of chaos to the laboratory test providing an experimental basis that can be developed for such applications as secure communications. This brief provides introductory information on sample chaotic circuits, includes coverage of their development, and the “gallery” section provides information on a wide range of circuits. Concise Guide to Chaotic Electronic Circuits will be useful to anyone running a laboratory class involving chaotic circuits and to students wishing to learn about them.
Chaotic lasers: The world's fastest dice
Murphy, Thomas E.; Roy, Rajarshi
2008-12-01
The dynamics of chaotic lasers can be harnessed to create a random-number generator that works at an astonishing rate. Such a generator could be implemented to make storage and transfer of data more secure at very high speeds.
Design of Digital Hybrid Chaotic Sequence Generator
Institute of Scientific and Technical Information of China (English)
RAO Nini; ZENG Dong
2004-01-01
The feasibility of the hybrid chaotic sequences as the spreading codes in code divided multiple access(CDMA) system is analyzed.The design and realization of the digital hybrid chaotic sequence generator by very high speed integrated circuit hardware description language(VHDL) are described.A valid hazard canceledl method is presented.Computer simulations show that the stable digital sequence waveforms can be produced.The correlations of the digital hybrid chaotic sequences are compared with those of m-sequences.The results show that the correlations of the digital hybrid chaotic sequences are almost as good as those of m-sequences.The works in this paper explored a road for the practical applications of chaos.
Binary black hole shadows, chaotic scattering and the Cantor set
Shipley, Jake O.; Dolan, Sam R.
2016-09-01
We investigate the qualitative features of binary black hole shadows using the model of two extremally charged black holes in static equilibrium (a Majumdar-Papapetrou solution). Our perspective is that binary spacetimes are natural exemplars of chaotic scattering, because they admit more than one fundamental null orbit, and thus an uncountably infinite set of perpetual null orbits which generate scattering singularities in initial data. Inspired by the three-disc model, we develop an appropriate symbolic dynamics to describe planar null geodesics on the double black hole spacetime. We show that a one-dimensional (1D) black hole shadow may be constructed through an iterative procedure akin to the construction of the Cantor set; thus the 1D shadow is self-similar. Next, we study non-planar rays, to understand how angular momentum affects the existence and properties of the fundamental null orbits. Taking slices through 2D shadows, we observe three types of 1D shadow: regular, Cantor-like, and highly chaotic. The switch from Cantor-like to regular occurs where outer fundamental orbits are forbidden by angular momentum. The highly chaotic part is associated with an unexpected feature: stable and bounded null orbits, which exist around two black holes of equal mass M separated by {a}1\\lt a\\lt \\sqrt{2}{a}1, where {a}1=4M/\\sqrt{27}. To show how this possibility arises, we define a certain potential function and classify its stationary points. We conjecture that the highly chaotic parts of the 2D shadow possess the Wada property. Finally, we consider the possibility of following null geodesics through event horizons, and chaos in the maximally extended spacetime.
Elliptic stars in a chaotic night
Jaeger, T
2010-01-01
We study homeomorphisms of the two-torus, homotopic to the identity, whose rotation set has non-empty interior. For such maps, we give a purely topological characterisation of elliptic islands in a chaotic sea in terms of local rotation subsets. We further show that the chaotic regime defined in this way cannot contain any Lyapunov stable points. In order to demonstrate our results, we introduce a parameter family inspired by an example of Misiurewicz and Ziemian.
Effects of Mismatched Parameter on Chaotic Synchronization
Institute of Scientific and Technical Information of China (English)
PENGJiang-hua; FANGJin-qing
2003-01-01
Chaos-based security communication has become one of the most interesting hot subjects for research of chaotic theory in real world since. In recent years, secure communication via synchronized chaos has been intensely studied. However, in practical application it is difficult to construct two complete identical chaotic systems since there are many reasons to induce parameter mismatch between two systems (response system and drive system).
Combination prediction method of chaotic time series
Institute of Scientific and Technical Information of China (English)
ZHAO DongHua; RUAN Jiong; CAI ZhiJie
2007-01-01
In the present paper, we propose an approach of combination prediction of chaotic time series. The method is based on the adding-weight one-rank local-region method of chaotic time series. The method allows us to define an interval containing a future value with a given probability, which is obtained by studying the prediction error distribution. Its effectiveness is shown with data generated by Logistic map.
IBFM for Ba isotopes and chaoticity
Energy Technology Data Exchange (ETDEWEB)
Bucurescu, D.; Cata-Danil, G.; Ivascu, M.; Ur, C.A. (Inst. of Atomic Physics, Bucharest (Romania)); Gizon, A.; Gizon, J. (Inst. des Sciences Nucleaires, 38 - Grenoble (France))
1992-08-01
Fluctuation properties have been analysed for the energy levels predicted by IBFM calculations in the Ba isotopes {sup 121}Ba to {sup 131}Ba. The results indicate, in general, a situation which is close to the chaotic limit. For the lighter isotopes studied (121 and 123), a phase transition is obtained in the low-spin, positive parity states, from a situation close to regularity at low excitation energies, towards chaoticity at higher excitations. (orig.).
IBFM for barium isotopes and chaoticity
Energy Technology Data Exchange (ETDEWEB)
Bucurescu, D.; Cata-Danil, G.; Ivascu, M.; Ur, C.A. (Institute of Atomic Physics, Bucharest (Romania)); Gizon, A.; Gizon, J. (Institute des Sciences Nucleaires, Grenoble (France))
1992-01-01
Fluctuation properties have been analysed for the energy levels predicted by IBFM calculations in the Ba isotopes {sup 121}Ba to {sup 131}Ba. The results are indicating, in general, a situation which is close to the chaotic limit. For the lighter isotopes studied (121 and 131), a phase transition is obtained in the low-spin, positive states, from a situation close to regularity at low excitation energies, towards chaoticity at higher excitations. (author).
IBFM for barium isotopes and chaoticity
Bucurescu, D.; Cata-Danil, G.; Ivascu, M.; Gizon, A.; Gizon, J.; UR, C. A.
Fluctuation properties have been analysed for the energy levels predicted by IBFM calculations in the Ba isotopes 121Ba to 131Ba. The results are indicating, in general, a situation which is close to the chaotic limit. For the lighter isotopes studied (121 and 131), a phase transition is obtained in the low-spin, positive states, from a situation close to regularity at low excitation energies, towards chaoticity at higher excitations.
On the timbre of chaotic algorithmic sounds
Sotiropoulos, Dimitrios A.; Sotiropoulos, Anastasios D.; Sotiropoulos, Vaggelis D.
Chaotic sound waveforms generated algorithmically are considered to study their timbre characteristics of harmonic and inharmonic overtones, loudness and onset time. Algorithms employed in the present work come from different first order iterative maps with parameters that generate chaotic sound waveforms. The generated chaotic sounds are compared with each other in respect of their waveforms' energy over the same time interval. Interest is focused in the logistic, double logistic and elliptic iterative maps. For these maps, the energy of the algorithmically synthesized sounds is obtained numerically in the chaotic region. The results show that for a specific parameter value in the chaotic region for each one of the first two maps, the calculated sound energy is the same. The energy, though, produced by the elliptic iterative map is higher than that of the other two maps everywhere in the chaotic region. Under the criterion of equal energy, the discrete Fourier transform is employed to compute for the logistic and double logistic iterative maps, a) the generated chaotic sound's power spectral density over frequency revealing the location (frequency) and relative loudness of the overtones which can be associated with fundamental frequencies of musical notes, and b) the generated chaotic sound's frequency dependent phase, which together with the overtones' frequency, yields the overtones' onset time. It is found that the synthesized overtones' loudness, frequency and onset time are totally different for the two generating algorithms (iterative maps) even though the sound's total generated power is equal. It is also demonstrated that, within each one of the iterative maps considered, the overtone characteristics are strongly affected by the choice of initial loudness.
Hierarchy in chaotic scattering in Hill's problem
Kovács, Z
1997-01-01
Hierarchic properties of chaotic scattering in a model of satellite encounters, studied first by Petit and Henon, are examined by decomposing the dwell time function and comparing scattering trajectories. The analysis reveals an (approximate) ternary organization in the chaotic set of bounded orbits and the presence of a stable island. The results can open the way for a calculation of global quantities characterizing the scattering process by using tools of the thermodynamic formalism.
两类混沌激光保密通信方案的性能分析%Performance analysis of two types of chaotic optical secure communication schemes
Institute of Scientific and Technical Information of China (English)
刘培洋; 赵清春; 殷洪玺
2012-01-01
High dimensional, broadband chaotic optical signal can be generated by a semiconductor laser with external disturbance, which is an ideal carrier for high-speed secure communications. The performances of chaotic optical secure communication systems are numerically studied by encrypting the message by chaos modulation (CMO) or chaos masking (CMS). The variation of the signal-to-noise ratio (SNR) and Q-factor are demonstrated when sinusoidal and digital messages are transmitted separately by CMO or CMS. The correlation coefficient as a function of modulation depth (MD) is discussed. The results show that the system performance varies for different MD or modulation frequency/rate and the performance of CMO system is better than that of CMS.%半导体激光器在外加扰动下,可以产生高维宽带的混沌激光信号,是实现高速保密通信的理想载波.数值研究了混沌调制和混沌隐藏两种信息加载方式下的混沌激光保密通信系统的性能,分析了两种信息加载方式下系统分别传输正弦信息和数字信息时的信噪比和Q因子的变化情况,研究了两种信息加载方式下系统的相关系数随调制深度的变化趋势.结果表明,不同的调制深度或调制频率/速率都会影响系统的性能,且混沌调制方式的系统性能优于混沌隐藏方式.
Chaotic motifs in gene regulatory networks.
Zhang, Zhaoyang; Ye, Weiming; Qian, Yu; Zheng, Zhigang; Huang, Xuhui; Hu, Gang
2012-01-01
Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations, if their dimensions are no less than 3. It is therefore puzzling that chaos has never been reported in GRNs in nature and is also extremely rare in models of GRNs. On the other hand, the topic of motifs has attracted great attention in studying biological networks, and network motifs are suggested to be elementary building blocks that carry out some key functions in the network. In this paper, chaotic motifs (subnetworks with chaos) in GRNs are systematically investigated. The conclusion is that: (i) chaos can only appear through competitions between different oscillatory modes with rivaling intensities. Conditions required for chaotic GRNs are found to be very strict, which make chaotic GRNs extremely rare. (ii) Chaotic motifs are explored as the simplest few-node structures capable of producing chaos, and serve as the intrinsic source of chaos of random few-node GRNs. Several optimal motifs causing chaos with atypically high probability are figured out. (iii) Moreover, we discovered that a number of special oscillators can never produce chaos. These structures bring some advantages on rhythmic functions and may help us understand the robustness of diverse biological rhythms. (iv) The methods of dominant phase-advanced driving (DPAD) and DPAD time fraction are proposed to quantitatively identify chaotic motifs and to explain the origin of chaotic behaviors in GRNs.
Spread Spectrum Communication with Chaotic Frequency Modulation
Volkovskii, Alexander R.; Tsimring, Lev S.; Rulkov, Nikolai F.; Langmore, Ian; Young, Stephen C.
We describe two different approaches to employ chaotic signals in spread-spectrum (SS) communication systems with phase and frequency modulation. In the first one a chaotic signal is used as a carrier. We demonstrate that using a feedback loop controller, the local chaotic oscillator in the receiver can be synchronized to the transmitter. The information can be transmitted using phase or frequency modulation of the chaotic carrier signal. In the second system the chaotic signal is used for frequency modulation of a voltage controlled oscillator (VCO) to provide a SS signal similar to frequency hopping systems. We show that in a certain parameter range the receiver VCO can be synchronized to the transmitter VCO using a relatively simple phase lock loop (PLL) circuit. The same PLL is used for synchronization of the chaotic oscillators. The information signal can be transmitted using a binary phase shift key (BPSK) or frequency shift key (BFSK) modulation of the frequency modulated carrier signal. Using an experimental circuit operating at radio frequency band and a computer modeling we study the bit error rate (BER) performance in a noisy channel as well as multiuser capability of the system.
Chaotic behavior in nonlinear polarization dynamics
Energy Technology Data Exchange (ETDEWEB)
David, D.; Holm, D.D.; Tratnik, M.V. (Los Alamos National Lab., NM (USA))
1989-01-01
We analyze the problem of two counterpropagating optical laser beams in a slightly nonlinear medium from the point of view of Hamiltonian systems; the one-beam subproblem is also investigated as a special case. We are interested in these systems as integrable dynamical systems which undergo chaotic behavior under various types of perturbations. The phase space for the two-beam problem is C{sup 2} {times} C{sup 2} when we restricted the the regime of travelling-wave solutions. We use the method of reduction for Hamiltonian systems invariant under one-parameter symmetry groups to demonstrate that the phase space reduces to the two-sphere S{sup 2} and is therefore completely integrable. The phase portraits of the system are classified and we also determine the bifurcations that modify these portraits; some new degenerate bifurcations are presented in this context. Finally, we introduce various physically relevant perturbations and use the Melnikov method to prove that horseshoe chaos and Arnold diffusion occur as consequences of these perturbations. 10 refs., 7 figs., 1 tab.
Chaotic radiation/turbulence interactions in flames
Energy Technology Data Exchange (ETDEWEB)
Menguec, M.P.; McDonough, J.M.
1998-11-01
In this paper, the authors present a review of their recent efforts to model chaotic radiation-turbulence interactions in flames. The main focus is to characterize soot volume fraction fluctuations in turbulent diffusion flames, as they strongly contribute to these interaction. The approach is based on the hypothesis that the fluctuations of properties in turbulent flames are deterministic in nature, rather than random. The authors first discuss the theoretical details and then they briefly outline the experiments conducted to measure the scattered light signals from fluctuating soot particles along the axis of an ethylene-air diffusion flame. They compare the power spectra and time series obtained from experiments against the ad-hoc and rigorous models derived using a series of logistic maps. These logistic maps can be used in simulation of the fluctuations in these type of flames, without extensive computational effort or sacrifice of physical detail. Availability of accurate models of these kinds allows investigation of radiation-turbulence interactions at a more fundamental level than it was previously possible.
A Devaney Chaotic System Which Is Neither Distributively nor Topologically Chaotic
Institute of Scientific and Technical Information of China (English)
Chen Zhi-zhi; Liao Li; Wang Wei
2013-01-01
Weiss proved that Devaney chaos does not imply topological chaos and Oprocha pointed out that Devaney chaos does not imply distributional chaos. In this paper, by constructing a simple example which is Devaney chaotic but neither distributively nor topologically chaotic, we give a unified proof for the results of Weiss and Oprocha.
Iterative prediction of chaotic time series using a recurrent neural network
Energy Technology Data Exchange (ETDEWEB)
Essawy, M.A.; Bodruzzaman, M. [Tennessee State Univ., Nashville, TN (United States). Dept. of Electrical and Computer Engineering; Shamsi, A.; Noel, S. [USDOE Morgantown Energy Technology Center, WV (United States)
1996-12-31
Chaotic systems are known for their unpredictability due to their sensitive dependence on initial conditions. When only time series measurements from such systems are available, neural network based models are preferred due to their simplicity, availability, and robustness. However, the type of neutral network used should be capable of modeling the highly non-linear behavior and the multi-attractor nature of such systems. In this paper the authors use a special type of recurrent neural network called the ``Dynamic System Imitator (DSI)``, that has been proven to be capable of modeling very complex dynamic behaviors. The DSI is a fully recurrent neural network that is specially designed to model a wide variety of dynamic systems. The prediction method presented in this paper is based upon predicting one step ahead in the time series, and using that predicted value to iteratively predict the following steps. This method was applied to chaotic time series generated from the logistic, Henon, and the cubic equations, in addition to experimental pressure drop time series measured from a Fluidized Bed Reactor (FBR), which is known to exhibit chaotic behavior. The time behavior and state space attractor of the actual and network synthetic chaotic time series were analyzed and compared. The correlation dimension and the Kolmogorov entropy for both the original and network synthetic data were computed. They were found to resemble each other, confirming the success of the DSI based chaotic system modeling.
Application of chaotic noise reduction techniques to chaotic data trained by ANN
Indian Academy of Sciences (India)
C Chandra Shekara Bhat; M R Kaimal; T R Ramamohan
2001-10-01
We propose a novel method of combining artiﬁcial neural networks (ANNs) with chaotic noise reduction techniques that captures the metric and dynamic invariants of a chaotic time series, e.g. a time series obtained by iterating the logistic map in chaotic regimes. Our results indicate that while the feedforward neural network is capable of capturing the dynamical and metric invariants of chaotic time series within an error of about 25%, ANNs along with chaotic noise reduction techniques, such as Hammel’s method or the local projective method, can signiﬁcantly improve these results. This further suggests that the effort on the ANN to train data corresponding to complex structures can be signiﬁcantly reduced. This technique can be applied in areas like signal processing, data communication, image processing etc.
Institute of Scientific and Technical Information of China (English)
Wang Xing-Yuan; Bao Xue-Mei
2013-01-01
In this paper,we propose a novel block cryptographic scheme based on a spatiotemporal chaotic system and a chaotic neural network (CNN).The employed CNN comprises a 4-neuron layer called a chaotic neuron layer (CNL),where the spatiotemporal chaotic system participates in generating its weight matrix and other parameters.The spatiotemporal chaotic system used in our scheme is the typical coupled map lattice (CML),which can be easily implemented in parallel by hardware.A 160-bit-long binary sequence is used to generate the initial conditions of the CML.The decryption process is symmetric relative to the encryption process.Theoretical analysis and experimental results prove that the block cryptosystem is secure and practical,and suitable for image encryption.
Institute of Scientific and Technical Information of China (English)
Cang Shi-Jian; Chen Zeng-Qiang; Wu Wen-Juan
2009-01-01
This paper presents a non-autonomous hyper-chaotic system, which is formed by adding a periodic driving signal to a four-dimensional chaotic model extended from the Lorenz system. The resulting non-autonomous hyper-chaotic system can display any dynamic behaviour among the periodic orbits, intermittency, chaos and hyper-chaos by controlling the frequency of the periodic signal. The phenomenon has been well demonstrated by numerical simulations, bifurcation analysis and electronic circuit realization. Moreover, the system is concrete evidence for the presence of Pomeau-Manneville Type-Ⅰ intermittency and crisis-induced intermittency. The emergence of a different type of intermittency is similarly subjected to the frequency of periodic forcing. By statistical analysis, power scaling laws consisting in different intermittency are obtained for the lifetime in the laminar state between burst states.
Institute of Scientific and Technical Information of China (English)
史恩慧; 周丽珍; 周友成
2003-01-01
It is proved that there is no chaotic group actions on any topological space with free arc.In this paper the chaotic actions of the group like G×F,where F is a finite group,are studied.In particular,under a suitable assumption,if F is a cyclic group,then the topological space which admits a chaotic action of Z×F must admit a chaotic homeomorphism.A topological space which admits a chaotic group action but admits no chaotic homeomorphism is constructed.
New Canards Bursting and Canards Periodic-Chaotic Sequence
Institute of Scientific and Technical Information of China (English)
YOOER Chi-Feng; XU Jian-Xue; ZHANG Xin-Hua
2009-01-01
A trajectory following the repelling branch of an equilibrium or a periodic orbit is called a canards solution. Using a continuation method, we find a new type of canards bursting which manifests itself in an alternation between the oscillation phase following attracting the limit cycle branch and resting phase following a repelling fixed point branch in a reduced leech neuron model. Via periodic-chaotic alternating of infinite times, the number of windings within a canards bursting can approach infinity at a Gavrilov-Shilnikov homoclinic tangency bifurcation of a simple saddle limit cycle.
Chaotic expression dynamics implies pluripotency: when theory and experiment meet
Directory of Open Access Journals (Sweden)
Furusawa Chikara
2009-05-01
Full Text Available Abstract Background During normal development, cells undergo a unidirectional course of differentiation that progressively decreases the number of cell types they can potentially become. Pluripotent stem cells can differentiate into several types of cells, but terminally differentiated cells cannot differentiate any further. A fundamental problem in stem cell biology is the characterization of the difference in cellular states, e.g., gene expression profiles, between pluripotent stem cells and terminally differentiated cells. Presentation of the hypothesis To address the problem, we developed a dynamical systems model of cells with intracellular protein expression dynamics and interactions with each other. According to extensive simulations, cells with irregular (chaotic oscillations in gene expression dynamics have the potential to differentiate into other cell types. During development, such complex oscillations are lost successively, leading to a loss of pluripotency. These simulation results, together with recent single-cell-level measurements in stem cells, led us to the following hypothesis regarding pluripotency: Chaotic oscillation in the expression of some genes leads to cell pluripotency and affords cellular state heterogeneity, which is supported by itinerancy over quasi-stable states. Differentiation stabilizes these states, leading to a loss of pluripotency. Testing the hypothesis To test the hypothesis, it is crucial to measure the time course of gene expression levels at the single-cell level by fluorescence microscopy and fluorescence-activated cell sorting (FACS analysis. By analyzing the time series of single-cell-level expression data, one can distinguish whether the variation in protein expression level over time is due only to stochasticity in expression dynamics or originates from the chaotic dynamics inherent to cells, as our hypothesis predicts. By further analyzing the expression in differentiated cell types, one can
Construction and Verification of a Simple Smooth Chaotic System
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display different attractors with two unstable equilibrium points and four unstable equilibrium points respectively. Dynamical properties of this system are then studied. Furthermore, by applying the undetermined coefficient method, heteroclinic orbit of (S)hil'nikov's type in this system is found and the convergence of the series expansions of this heteroclinic orbit are proved in this article. The (S)hil'nikov's theorem guarantees that this system has Smale horseshoes and the horseshoe chaos.
Chaotic mechanics in systems with impacts and friction
Blazejczyk-Okolewska, Barbara; Kapitaniak, Tomasz; Wojewoda, Jerzy
1999-01-01
This book is devoted to the theory of chaotic oscillations in mechanical systems. Detailed descriptions of the basic types of nonlinearity - impacts and dry friction - are presented. The properties of such behavior are discussed, and the numerical and experimental results obtained by the authors are presented.The dynamic properties of systems described here can be useful in the proper design and use of mechanics where such behavior still creates problems.This book will be very useful for anyone with a fundamental knowledge of nonlinear mechanics who is beginning research in the field.
Linear optimal control of continuous time chaotic systems.
Merat, Kaveh; Abbaszadeh Chekan, Jafar; Salarieh, Hassan; Alasty, Aria
2014-07-01
In this research study, chaos control of continuous time systems has been performed by using dynamic programming technique. In the first step by crossing the response orbits with a selected Poincare section and subsequently applying linear regression method, the continuous time system is converted to a discrete type. Then, by solving the Riccati equation a sub-optimal algorithm has been devised for the obtained discrete chaotic systems. In the next step, by implementing the acquired algorithm on the quantized continuous time system, the chaos has been suppressed in the Rossler and AFM systems as some case studies.
Extended Logistic Chaotic Sequence and Its Performance Analysis
Institute of Scientific and Technical Information of China (English)
ZHANG Xuefeng; FAN Jiulun
2007-01-01
In order to improve performance and security of image encryption algorithm effectively based on chaotic sequences, an extended chaotic sequence generating method is presented based on logistic chaotic system using Bernstein form Bezier curve generating algorithm. In order to test the pseudorandom performance of the extended chaotic sequence, we also analyze random performance, autocorrelation performance, and balance performance of the extended chaotic sequence. Simulation results show that the extended chaotic sequence generated using our method is pseudorandom and its correlation performance and balance performance are good. As an application, we apply the extended chaotic sequence in image encryption algorithm, the simulation results show that the performance of the encrypted image using our method is better than that using logistic chaotic sequence.
The formation of composite chaotic multiattractors containing inhomogeneities
Prokopenko, V. G.
2017-08-01
Two methods for introducing inhomogeneities into composite chaotic multiattractors have been proposed. The first method makes it possible to change the mutual arrangement of multiattractor elements. The second method allows one to preset differences between chaotic attractors forming a multiattractor.
SWITCHING CONTROL:FROM SIMPLE RULES TO COMPLEX CHAOTIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
L(U) Jinhu
2003-01-01
This paper reviews and introduces some simple switching piecewise-linear controllers, which can generate complex chaotic behaviors from simple switching systems. The mechanism of simple switching rules creating complex chaotic behaviors is further investigated.
Pei, Yan
2015-01-01
We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.
Directory of Open Access Journals (Sweden)
Yan Pei
2015-01-01
Full Text Available We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC algorithm, interactive chaotic evolution (ICE that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.
Chaotic dynamics of flexible Euler-Bernoulli beams
Energy Technology Data Exchange (ETDEWEB)
Awrejcewicz, J., E-mail: awrejcew@p.lodz.pl [Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland and Department of Vehicles, Warsaw University of Technology, 84 Narbutta St., 02-524 Warsaw (Poland); Krysko, A. V., E-mail: anton.krysko@gmail.com [Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov (Russian Federation); Kutepov, I. E., E-mail: iekutepov@gmail.com; Zagniboroda, N. A., E-mail: tssrat@mail.ru; Dobriyan, V., E-mail: Dobriy88@yandex.ru; Krysko, V. A., E-mail: tak@san.ru [Department of Mathematics and Modeling, Saratov State Technical University, Politehnicheskaya 77, 410054 Saratov (Russian Federation)
2013-12-15
Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions is carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ω{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.
Exponential H∞ synchronization and state estimation for chaotic systems via a unified model.
Liu, Meiqin; Zhang, Senlin; Fan, Zhen; Zheng, Shiyou; Sheng, Weihua
2013-07-01
In this paper, H∞ synchronization and state estimation problems are considered for different types of chaotic systems. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these chaotic systems, such as Hopfield neural networks, cellular neural networks, Chua's circuits, unified chaotic systems, Qi systems, chaotic recurrent multilayer perceptrons, etc. Based on the H∞ performance analysis of this unified model using the linear matrix inequality approach, novel state feedback controllers are established not only to guarantee exponentially stable synchronization between two unified models with different initial conditions but also to reduce the effect of external disturbance on the synchronization error to a minimal H∞ norm constraint. The state estimation problem is then studied for the same unified model, where the purpose is to design a state estimator to estimate its states through available output measurements so that the exponential stability of the estimation error dynamic systems is guaranteed and the influence of noise on the estimation error is limited to the lowest level. The parameters of these controllers and filters are obtained by solving the eigenvalue problem. Most chaotic systems can be transformed into this unified model, and H∞ synchronization controllers and state estimators for these systems are designed in a unified way. Three numerical examples are provided to show the usefulness of the proposed H∞ synchronization and state estimation conditions.
A comparative study of chaotic and white noise signals in digital watermarking
Energy Technology Data Exchange (ETDEWEB)
Mooney, Aidan [Department of Computer Science, NUI Maynooth, Co. Kildare (Ireland)], E-mail: amooney@cs.nuim.ie; Keating, John G. [Department of Computer Science, NUI Maynooth, Co. Kildare (Ireland)], E-mail: john.keating@nuim.ie; Pitas, Ioannis [Department of Informatics, Aristole University of Thessaloniki, P.O. Box 451, Thessaloniki 540 06 (Greece)], E-mail: pitas@zeus.csd.auth.gr
2008-03-15
Digital watermarking is an ever increasing and important discipline, especially in the modern electronically-driven world. Watermarking aims to embed a piece of information into digital documents which their owner can use to prove that the document is theirs, at a later stage. In this paper, performance analysis of watermarking schemes is performed on white noise sequences and chaotic sequences for the purpose of watermark generation. Pseudorandom sequences are compared with chaotic sequences generated from the chaotic skew tent map. In particular, analysis is performed on highpass signals generated from both these watermark generation schemes, along with analysis on lowpass watermarks and white noise watermarks. This analysis focuses on the watermarked images after they have been subjected to common image distortion attacks. It is shown that signals generated from highpass chaotic signals have superior performance than highpass noise signals, in the presence of such attacks. It is also shown that watermarks generated from lowpass chaotic signals have superior performance over the other signal types analysed.
Barnes, Rory; Greenberg, Richard; Quinn, Thomas R; Raymond, Sean N
2015-01-01
We present N-body simulations of resonant planets with inclined orbits that show chaotically evolving eccentricities and inclinations that can persist for at least 10 Gyr. A wide range of behavior is possible, from fast, low amplitude variations to systems in which eccentricities reach 0.9999 and inclinations 179.9 degrees. While the orbital elements evolve chaotically, at least one resonant argument always librates. We show that the HD 73526, HD 45364 and HD 60532 systems may be in chaotically-evolving resonances. Chaotic evolution is apparent in the 2:1, 3:1 and 3:2 resonances, and for planetary masses from lunar- to Jupiter-mass. In some cases, orbital disruption occurs after several Gyr, implying the mechanism is not rigorously stable, just long-lived relative to the main sequence lifetimes of solar-type stars. Planet-planet scattering appears to yield planets in inclined resonances that evolve chaotically in about 0.5% of cases. These results suggest that 1) approximate methods for identifying unstable o...
Shadowing Lemma and Chaotic Orbit Determination
Spoto, Federica
2015-01-01
Orbit determination is possible for a chaotic orbit of a dynamical system, given a finite set of observations, provided the initial conditions are at the central time. In a simple discrete model, the standard map, we tackle the problem of chaotic orbit determination when observations extend beyond the predictability horizon. If the orbit is hyperbolic, a shadowing orbit is computed by the least squares orbit determination. We test both the convergence of the orbit determination iterative procedure and the behaviour of the uncertainties as a function of the maximum number $n$ of map iterations observed. When the initial conditions belong to a chaotic orbit, the orbit determination is made impossible by numerical instability beyond a computability horizon, which can be approximately predicted by a simple formula. Moreover, the uncertainty of the results is sharply increased if a dynamical parameter is added to the initial conditions as parameter to be estimated. The uncertainty of the dynamical parameter decrea...
Controlling chaotic transients: Yorke's game of survival
DEFF Research Database (Denmark)
Aguirre, Jacobo; D'ovidio, Francesco; Sanjuán, Miguel A. F.
2004-01-01
We consider the tent map as the prototype of a chaotic system with escapes. We show analytically that a small, bounded, but carefully chosen perturbation added to the system can trap forever an orbit close to the chaotic saddle, even in presence of noise of larger, although bounded, amplitude......, the dynamics diverge, leaving a relatively safe region, and we say the protagonist loses. What makes survival difficult is that the adversary is allowed stronger "actions" than the protagonist. What makes survival possible is (i) the background dynamics (the tent map here) are chaotic and (ii) the protagonist...... knows the action of the adversary in choosing his response and is permitted to choose the initial point x(0) of the game. We use the "slope 3" tent map in an example of this problem. We show that it is possible for the protagonist to survive....
Synchronization of chaotic systems with different order.
Femat, Ricardo; Solís-Perales, Gualberto
2002-03-01
The chaotic synchronization of third-order systems and second-order driven oscillator is studied in this paper. Such a problem is related to synchronization of strictly different chaotic systems. We show that dynamical evolution of second-order driven oscillators can be synchronized with the canonical projection of a third-order chaotic system. In this sense, it is said that synchronization is achieved in reduced order. Duffing equation is chosen as slave system whereas Chua oscillator is defined as master system. The synchronization scheme has nonlinear feedback structure. The reduced-order synchronization is attained in a practical sense, i.e., the difference e=x(3)-x(1)(') is close to zero for all time t> or =t(0)> or =0, where t(0) denotes the time of the control activation.
Controlled transitions between cupolets of chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Morena, Matthew A., E-mail: matthew.morena@wildcats.unh.edu; Short, Kevin M.; Cooke, Erica E. [Integrated Applied Mathematics Program, University of New Hampshire, Durham, New Hampshire 03824 (United States)
2014-03-15
We present an efficient control scheme that stabilizes the unstable periodic orbits of a chaotic system. The resulting orbits are known as cupolets and collectively provide an important skeleton for the dynamical system. Cupolets exhibit the interesting property that a given sequence of controls will uniquely identify a cupolet, regardless of the system's initial state. This makes it possible to transition between cupolets, and thus unstable periodic orbits, simply by switching control sequences. We demonstrate that although these transitions require minimal controls, they may also involve significant chaotic transients unless carefully controlled. As a result, we present an effective technique that relies on Dijkstra's shortest path algorithm from algebraic graph theory to minimize the transients and also to induce certainty into the control of nonlinear systems, effectively providing an efficient algorithm for the steering and targeting of chaotic systems.
Controlled transitions between cupolets of chaotic systems.
Morena, Matthew A; Short, Kevin M; Cooke, Erica E
2014-03-01
We present an efficient control scheme that stabilizes the unstable periodic orbits of a chaotic system. The resulting orbits are known as cupolets and collectively provide an important skeleton for the dynamical system. Cupolets exhibit the interesting property that a given sequence of controls will uniquely identify a cupolet, regardless of the system's initial state. This makes it possible to transition between cupolets, and thus unstable periodic orbits, simply by switching control sequences. We demonstrate that although these transitions require minimal controls, they may also involve significant chaotic transients unless carefully controlled. As a result, we present an effective technique that relies on Dijkstra's shortest path algorithm from algebraic graph theory to minimize the transients and also to induce certainty into the control of nonlinear systems, effectively providing an efficient algorithm for the steering and targeting of chaotic systems.
Modified chaotic ant swarm to function optimization
Institute of Scientific and Technical Information of China (English)
LI Yu-ying; WEN Qiao-yan; LI Li-xiang
2009-01-01
The chaotic ant swarm algorithm (CAS) is an optimization algorithm based on swarm intelligence theory, and it is inspired by the chaotic and self-organizing behavior of the ants in nature. Based on the analysis of the properties of the CAS, this article proposes a variation on the CAS called the modified chaotic ant swarm (MCAS), which employs two novel strategies to significantly improve the performance of the original algorithm. This is achieved by restricting the variables to search ranges and making the global best ant to learn from different ants' best information in the end. The simulation of the MCAS on five benchmark functions shows that the MCAS improves the precision of the solution.
a Multiple-Plaintexts Chaotic Cryptosystem
Wang, Xing-Yuan; Tan, Yisong
2013-10-01
In recent years, a lot of chaotic cryptosystems have been proposed. However, most of these cryptosystems can encrypt only one plaintext in one encryption process. We call these cryptosystems single-plaintext-oriented cryptosystems. In this paper, the authors propose a new chaotic cryptosystem which can encrypt multiple plaintexts in one encryption process. The proposed cryptosystem is dedicated to encrypting multiple plaintexts in the situation of transmitting multiple secret files over public data communication network in one secure transmission. Experiments and theoretic analysis show that the proposed cryptosystem possesses high security and fast performance speed. They also show that the proposed cryptosystem is more secure than single-plaintext-oriented chaotic cryptosystems in this special situation.
Stabilizing chaotic-scattering trajectories using control
Lai, Ying-Cheng; Tél, Tamás; Grebogi, Celso
1993-08-01
The method of stabilizing unstable periodic orbits in chaotic dynamical systems by Ott, Grebogi, and Yorke (OGY) is applied to control chaotic scattering in Hamiltonian systems. In particular, we consider the case of nonhyperbolic chaotic scattering, where there exist Kolmogorov-Arnold-Moser (KAM) surfaces in the scattering region. It is found that for short unstable periodic orbits not close to the KAM surfaces, both the probability that a particle can be controlled and the average time to achieve control are determined by the initial exponential decay rate of particles in the hyperbolic component. For periodic orbits near the KAM surfaces, due to the stickiness effect of the KAM surfaces on particle trajectories, the average time to achieve control can greatly exceed that determined by the hyperbolic component. The applicability of the OGY method to stabilize intermediate complexes of classical scattering systems is suggested.
Chaotic behavior learning of Chua's circuit
Institute of Scientific and Technical Information of China (English)
Sun Jian-Cheng
2012-01-01
Least-square support vector machines (LS-SVM) are applied for learning the chaotic behavior of Chua's circuit.The system is divided into three multiple-input single-output (MISO) structures and the LS-SVM are trained individually.Comparing with classical approaches,the proposed one reduces the structural complexity and the selection of parameters is avoided.Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation.Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua's circuit state variables,and exhibit the chaotic attractors under the autonomous working mode.
Maximizing the security of chaotic optical communications.
Hou, T T; Yi, L L; Yang, X L; Ke, J X; Hu, Y; Yang, Q; Zhou, P; Hu, W S
2016-10-03
The practical application of chaotic optical communications has been limited by two aspects: the difficulty in concealing the time delay - a critical security parameter in feedback chaotic systems, and the difficulty of significantly enlarging the key space without complicating the implementation. Here we propose an architecture to break the above limits. By introducing a frequency-dependent group delay module with frequency tuning resolution of 1 MHz into the chaotic feedback loop, we demonstrate excellent time delay concealment effect, and an additional huge key space of 1048 can be achieved at the same time. The effectiveness is proved by both numerical simulation and experiment. Besides, the proposed scheme is compatible with the existing commercial optical communication systems, thus pave the way for high-speed secure optical communications.
A minimum principle for chaotic dynamical systems
Bracken, Paul; Góra, Paweł; Boyarsky, Abraham
2002-06-01
Discrete time dynamical systems generated by the iteration of nonlinear maps, such as the logistic map or the tent map, provide interesting examples of chaotic systems. But what is the physical principle behind the emergence of these maps? In the continuous time settings, differential equations of mechanics arise from the minimization of the energy function (Hamiltonian). However, there is no general physical principle for the discrete time analogue of differential equations, namely, maps. In this note, we present an approach to this problem. Using a natural definition of energy for chaotic systems, we minimize energy subject to the constraint that the observed dynamical system has a known entropy. We consider the case where the natural invariant measure is Lebesgue. Invoking the Euler-Lagrange equation, we derive a nonlinear second order differential equation whose solution is the chaotic map that minimizes energy.
Extracting periodic driving signal from chaotic noise
Institute of Scientific and Technical Information of China (English)
MU Jing; TAO Chao; DU Gonghuan
2003-01-01
After periodic signals pass through some nonlinear systems, they are usually transformed into noise-like and wide-band chaotic signals. The discrete spectrums of the original periodic signals are often covered by the chaotic spectrums. Recovering the periodic driving signals from the chaotic signals is important not only in theory but also in practical applications. Based on the modeling theory of nonlinear dynamic system, a "polynomial-simple harmonic drive" non-autonomous equation (P-S equation) to approximate the original system is proposed and the approximation error between P-S equation and the original system is obtained. By changing the drive frequency, we obtain the curve of the approximation error vs. drive frequency. Based on the relation between this curve and the spectrums of the original periodic signals, the spectrum of the original driving signal is extracted and the original signal is recovered.
CHAOTIC CONTROL OF NONLINEAR SYSTEMS BASED ON IMPROVED CORRELATIVITY
Institute of Scientific and Technical Information of China (English)
ZhouZiaoan; ZhangJihong
2003-01-01
Chaotic sequences are basically ergodic random esquences.By improving correlativity of a chaotic signal,the chaotic dynamic system can be controlled to converge to its equilibrium point and,more significantly,to its multi-periodic orbits.Mathematical theory analysis is carried out and some computer simulation results are provided to support such controllability of the chaotic Henon system and the discrete coupled map lattice.
Capability Analysis of Chaotic Mutation and Its Self－Adaption
Institute of Scientific and Technical Information of China (English)
YANGLi－Jiang; CHENTian－Lun
2002-01-01
Through studying several kinds of chaotic mappings distributions of orbital points,we analyze the capabuility of the chaotic mutations based on these mappings,Numerical experiments support our conclusions very well.The capability analysis also led to a self-adaptive mechanism of chaotic mutation.The introducing of the self-adaptive chaotic mutation can improve the performance of genetic algorithm very prominently.
Projective synchronization of chaotic systems with bidirectional nonlinear coupling
Indian Academy of Sciences (India)
Mohammada Ali Khan; Swarup Poria
2013-09-01
This paper presents a new scheme for constructing bidirectional nonlinear coupled chaotic systems which synchronize projectively. Conditions necessary for projective synchronization (PS) of two bidirectionally coupled chaotic systems are derived using Lyapunov stability theory. The proposed PS scheme is discussed by taking as examples the so-called unified chaotic model, the Lorenz–Stenflo system and the nonautonomous chaotic Van der Pol oscillator. Numerical simulation results are presented to show the efficiency of the proposed synchronization scheme.
Bogomolov, Sergey A.; Slepnev, Andrei V.; Strelkova, Galina I.; Schöll, Eckehard; Anishchenko, Vadim S.
2017-02-01
We explore the bifurcation transition from coherence to incoherence in ensembles of nonlocally coupled chaotic systems. It is firstly shown that two types of chimera states, namely, amplitude and phase, can be found in a network of coupled logistic maps, while only amplitude chimera states can be observed in a ring of continuous-time chaotic systems. We reveal a bifurcation mechanism by analyzing the evolution of space-time profiles and the coupling function with varying coupling coefficient and formulate the necessary and sufficient conditions for realizing the chimera states in the ensembles.
Synchronization between two different noise-perturbed chaotic systems with unknown parameters
Jia, Fei-Lei; Xu, Wei; Du, Lin
2007-11-01
In this paper, a general method of synchronizing noise-perturbed chaotic systems with unknown parameters is proposed. Based on the LaSalle-type invariance principle for stochastic differential equations and by employing a combination of feedback control and adaptive control, some sufficient conditions of chaos synchronization between these noise-perturbed systems with unknown parameters are established. The model used in the research is the chaotic system, but the method is also applicable to the hyperchaotic systems. Unified system and noise-perturbed Rössler system, hyperchaotic Chen system and noise-perturbed hyperchaotic Rössler system are taken for illustrative examples to demonstrate this technique.
Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Perez-Pinacho, Claudia A.
2014-06-01
The main issue of this work is related with the design of a class of nonlinear observer in order to synchronize chaotic dynamical systems in a master-slave scheme, considering different initial conditions. The oscillator of Chen is proposed as a benchmark model and a bounded-type observer is proposed to reach synchronicity between both two chaotic systems. The proposed observer contains a proportional and sigmoid form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Some numerical simulations were carrying out in order to show the operation of the proposed methodology, with possible applications to secure data communications issues.
Extracting messages masked by chaotic signals of time-delay systems.
Zhou, C; Lai, C H
1999-07-01
We show how to extract messages masked by a chaotic signal of a time-delay system with very high dimensions and many positive Lyapunov exponents. Using a special embedding coordinate, the infinite-dimensional phase space of the time-delay system is projected onto a special three-dimensional space, which enables us to identify the time delay of the system from the transmitted signal and reconstruct the chaotic dynamics to unmask the hidden message successfully. The message extraction procedure is illustrated by simulations with the Mackey-Glass time-delay system for two types of masking schemes and different kinds of messages.
Chaotic Behavior in a Flexible Assembly Line of a Manufacturing System
Directory of Open Access Journals (Sweden)
M. Sajid
2015-12-01
Full Text Available The purpose of the present work is to study the chaotic behavior in a flexible assembly line of a manufacturing system. A flexible assembly line can accommodate a variety of product types. Result analysis is performed to obtain time persistent data. The behavior of the system is observed for Work-In-Process, as assembling systems are sensitive during processing. It is found that the average Lyapunov exponent is positive in the considered case, and thus chaotic behavior may be present in flexible assembly lines.
Random matrix theory of quantum transport in chaotic cavities with nonideal leads
Jarosz, Andrzej; Vidal, Pedro; Kanzieper, Eugene
2015-05-01
We determine the joint probability density function (JPDF) of reflection eigenvalues in three Dyson's ensembles of normal-conducting chaotic cavities coupled to the outside world through both ballistic and tunnel point contacts. Expressing the JPDF in terms of hypergeometric functions of matrix arguments (labeled by the Dyson index β ), we further show that reflection eigenvalues form a determinantal ensemble at β =2 and a new type of a Pfaffian ensemble at β =4 . As an application, we derive a simple analytic expression for the concurrence distribution describing production of orbitally entangled electrons in chaotic cavities with tunnel point contacts when time-reversal symmetry is preserved.
Synchronizing the information content of a chaotic map and flow via symbolic dynamics.
Corron, Ned J; Pethel, Shawn D; Myneni, Krishna
2002-09-01
In this paper we report an extension to the concept of generalized synchronization for coupling different types of chaotic systems, including maps and flows. This broader viewpoint takes disparate systems to be synchronized if their information content is equivalent. We use symbolic dynamics to quantize the information produced by each system and compare the symbol sequences to establish synchronization. A general architecture is presented for drive-response coupling that detects symbols produced by a chaotic drive oscillator and encodes them in a response system using the methods of chaos control. We include experimental results demonstrating synchronization of information content in an electronic oscillator circuit driven by a logistic map.
Stabilization of generalized fractional order chaotic systems using state feedback control
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Wajdi M. E-mail: wajdi@sharjah.ac.ae; El-Khazali, Reyad E-mail: khazali@ece.ac.ae; Al-Assaf, Yousef E-mail: yassaf@aus.ac.ae
2004-10-01
In this paper, we address the problem of chaos control of three types of fractional order systems using simple state feedback gains. Electronic chaotic oscillators, mechanical 'jerk' systems, and the Chen system are investigated when they assume generalized fractional orders. We design the static gains to place the eigenvalues of the system Jacobian matrices in a stable region whose boundaries are determined by the orders of the fractional derivatives. We numerically demonstrate the effectiveness of the controller in eliminating the chaotic behavior from the state trajectories, and driving the states to the nearest equilibrium point in the basin of attraction. For the recently introduced Chen system, in particular, we demonstrate that with a proper choice of model parameters, chaotic behavior is preserved when the system order becomes fractional. Both state and output feedback controllers are then designed to stabilize a generalized fractional order Chen system.
Elementary quadratic chaotic flows with a single non-hyperbolic equilibrium
Energy Technology Data Exchange (ETDEWEB)
Wei, Zhouchao, E-mail: weizhouchao@163.com [School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074 (China); College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124 (China); Mathematical Institute, University of Oxford, Oxford (United Kingdom); Sprott, J.C., E-mail: sprott@physics.wisc.edu [Department of Physics, University of Wisconsin, Madison, WI 53706 (United States); Chen, Huai [Faculty of Earth Sciences, China University of Geosciences, Wuhan, 430074 (China)
2015-10-02
Highlights: • A kind of jerk equations are proposed. • Chaos can occur with all types of a non-hyperbolic equilibrium. • The mechanism of generating chaos is discussed. • Feigenbaum's constant explains the identified chaotic flows. - Abstract: This paper describes a class of third-order explicit autonomous differential equations, called jerk equations, with quadratic nonlinearities that can generate a catalog of nine elementary dissipative chaotic flows with the unusual feature of having a single non-hyperbolic equilibrium. They represent an interesting sub-class of dynamical systems that can exhibit many major features of regular and chaotic motion. The proposed systems are investigated through numerical simulations and theoretical analysis. For these jerk dynamical systems, a certain amount of nonlinearity is sufficient to produce chaos through a sequence of period-doubling bifurcations.
Multiple sequence alignment based on combining genetic algorithm with chaotic sequences.
Gao, C; Wang, B; Zhou, C J; Zhang, Q
2016-06-24
In bioinformatics, sequence alignment is one of the most common problems. Multiple sequence alignment is an NP (nondeterministic polynomial time) problem, which requires further study and exploration. The chaos optimization algorithm is a type of chaos theory, and a procedure for combining the genetic algorithm (GA), which uses ergodicity, and inherent randomness of chaotic iteration. It is an efficient method to solve the basic premature phenomenon of the GA. Applying the Logistic map to the GA and using chaotic sequences to carry out the chaotic perturbation can improve the convergence of the basic GA. In addition, the random tournament selection and optimal preservation strategy are used in the GA. Experimental evidence indicates good results for this process.
REVIEWS OF TOPICAL PROBLEMS: On the use of chaotic synchronization for secure communication
Koronovskii, Aleksei A.; Moskalenko, Olga I.; Hramov, Aleksandr E.
2009-12-01
Research on the secure communication applications of chaotic synchronization is reviewed. A number of secure communication methods and devices using different types of synchronous behavior are examined. For the purpose of comparing existing methods, quantitative characteristics of operating capacity of various schemes are introduced and estimated. An extremely noise-stable secure information transmission method, based on the phenomenon of generalized chaos synchronization, is proposed. All of the methods considered are systematically checked for efficiency for the first time by numerically simulating unidirectionally coupled chaotic Rössler systems selected for transmitting and receiving oscillators. The key advantages and disadvantages of secure information transmission schemes using synchronized chaotic oscillations are discussed. The experimental data gathered in this field are also reviewed.
Chaotic Flows Correlation effects and coherent structures
Bakunin, Oleg G
2011-01-01
The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.
Chaotic Maps Dynamics, Fractals, and Rapid Fluctuations
Chen, Goong
2011-01-01
This book consists of lecture notes for a semester-long introductory graduate course on dynamical systems and chaos taught by the authors at Texas A&M University and Zhongshan University, China. There are ten chapters in the main body of the book, covering an elementary theory of chaotic maps in finite-dimensional spaces. The topics include one-dimensional dynamical systems (interval maps), bifurcations, general topological, symbolic dynamical systems, fractals and a class of infinite-dimensional dynamical systems which are induced by interval maps, plus rapid fluctuations of chaotic maps as a
Trend prediction of chaotic time series
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Trend prediction of chaotic ti me series is anin-teresting probleminti me series analysis andti me se-ries data mining(TSDM)fields[1].TSDM-basedmethods can successfully characterize and predictcomplex,irregular,and chaotic ti me series.Somemethods have been proposed to predict the trend ofchaotic ti me series.In our knowledge,these meth-ods can be classified into t wo categories as follows.The first category is based on the embeddedspace[2-3],where rawti me series data is mapped to areconstructed phase spac...
Searching of Chaotic Elements in Hydrology
Directory of Open Access Journals (Sweden)
Sorin VLAD
2014-03-01
Full Text Available Chaos theory offers new means of understanding and prediction of phenomena otherwise considered random and unpredictable. The signatures of chaos can be isolated by performing nonlinear analysis of the time series available. The paper presents the results obtained by conducting a nonlinear analysis of the time series of daily Siret river flow (located in the North-Eastern part of Romania. The time series analysis is recorded starting with January 1999 to July 2009. The attractor is embedded in the reconstructed phase space then the chaotic dynamics is revealed computing the chaotic invariants - correlation dimension and the maximum Lyapunov Exponent.
Higgs Vacuum Stability and Modified Chaotic Inflation
Saha, Abhijit Kumar
2016-01-01
The issue of electroweak vacuum stability is studied in presence of a scalar field which participates in modifying the minimal chaotic inflation model. It is shown that the threshold effect on the Higgs quartic coupling originating from the Higgs-inflaton sector interaction can essentially make the electroweak vacuum stable upto the Planck scale. On the other hand we observe that the new physics parameters in this combined framework are enough to provide deviation from the minimal chaotic inflation predictions so as to keep it consistent with recent observation by Planck 2015.
Chaotic Load Series Forecasting Based on MPMR
Institute of Scientific and Technical Information of China (English)
Liu Zunxiong; Cheng Quanhua; Zhang Deyun
2006-01-01
Minimax probability machine regression (MPMR) was proposed for chaotic load time series global prediction. In MPMR, regression function maximizes the minimum probability that future predication will be within an ε to the true regression function. After exploring the principle of MPMR, and verifying the chaotic property of the load series from a certain power system, one-day-ahead predictions for 24 time points next day were done with MPMR. The results demonstrate that MPMP has satisfactory prediction efficiency. Kernel function shape parameter and regression tube value may influence the MPMR-based system performance. In the experiments, cross validation was used to choose the two parameters.
Generalized Synchronization of Diverse Structure Chaotic Systems
Institute of Scientific and Technical Information of China (English)
KADIR Abdurahman; WANG Xing-Yuan; ZHAO Yu-Zhang
2011-01-01
@@ Generalized synchronization between two diverse structures of chaotic systems possesses significance in the research of synchronization.We propose an approach based on the Lyapunov stability theory to study it.This method can be used widely.Numerical examples are given to demonstrate the effectiveness of this approach.%Generalized synchronization between two diverse structures of chaotic systems possesses significance in the research of synchronization. We propose an approach based on the Lyapunov stability theory to study it. This method can be used widely. Numerical examples are given to demonstrate the effectiveness of this approach.
Will Quantum Cosmology Resurrect Chaotic Inflation Model?
Kim, Sang Pyo; Kim, Won
2016-07-01
The single field chaotic inflation model with a monomial power greater than one seems to be ruled out by the recent Planck and WMAP CMB data while Starobinsky model with a higher curvature term seems to be a viable model. Higher curvature terms being originated from quantum fluctuations, we revisit the quantum cosmology of the Wheeler-DeWitt equation for the chaotic inflation model. The semiclassical cosmology emerges from quantum cosmology with fluctuations of spacetimes and matter when the wave function is peaked around the semiclassical trajectory with quantum corrections a la the de Broglie-Bohm pilot theory.
Will quantum cosmology resurrect chaotic inflation model?
Kim, Sang Pyo
2016-01-01
The single field chaotic inflation model with a monomial power greater than one seems to be ruled out by the recent Planck and WMAP CMB data while Starobinsky model with a higher curvature term seems to be a viable model. Higher curvature terms being originated from quantum fluctuations, we revisit the quantum cosmology of the Wheeler-DeWitt equation for the chaotic inflation model. The semiclassical cosmology emerges from quantum cosmology with fluctuations of spacetimes and matter when the wave function is peaked around the semiclassical trajectory with quantum corrections a la the de Broglie-Bohm pilot theory.
An adaptive strategy for controlling chaotic system
Institute of Scientific and Technical Information of China (English)
曹一家; 张红先
2003-01-01
This paper presents an adaptive strategy for controlling chaotic systems. By employing the phase space reconstruction technique in nonlinear dynamical systems theory, the proposed strategy transforms the nonlinear system into canonical form, and employs a nonlinear observer to estimate the uncertainties and disturbances of the nonlinear system, and then establishes a state-error-like feedback law. The developed control scheme allows chaos control in spite of modeling errors and parametric variations. The effectiveness of the proposed approach has been demonstrated through its applications to two well-known chaotic systems : Duffing oscillator and Rǒssler chaos.
Chaotic inflation with curvaton induced running
DEFF Research Database (Denmark)
Sloth, Martin Snoager
2014-01-01
While dust contamination now appears as a likely explanation of the apparent tension between the recent BICEP2 data and the Planck data, we will here explore the consequences of a large running in the spectral index as suggested by the BICEP2 collaboration as an alternative explanation...... of the apparent tension, but which would be in conflict with prediction of the simplest model of chaotic inflation. The large field chaotic model is sensitive to UV physics, and the nontrivial running of the spectral index suggested by the BICEP2 collaboration could therefore, if true, be telling us some...
CHAOTIC BELT PHENOMENA IN NONLINEAR ELASTIC BEAM
Institute of Scientific and Technical Information of China (English)
张年梅; 杨桂通
2003-01-01
The chaotic motions of axial compressed nonlinear elastic beam subjected totransverse load were studied. The damping force in the system is nonlinear. Consideringmaterial and geometric nonlinearity, nonlinear governing equation of the system wasderived. By use of nonlinear Galerkin method, differential dynamic system was set up.Melnikov method was used to analyze the characters of the system. The results showed thatchaos may occur in the system when the load parameters P0 and f satisfy some conditions.The zone of chaotic motion was belted. The route from subharmonic bifurcation to chaoswas analyzed. The critical conditions that chaos occurs were determined.
Chaotic scattering off a rotating target
Energy Technology Data Exchange (ETDEWEB)
Meyer, N.; Benet, L.; Lipp, C.; Trautmann, D.; Jung, C.; Seligman, T.H. [Inst. fuer Theor. Phys., Basel Univ. (Switzerland)
1995-05-07
We study the classical scattering of a point particle from one and two rotating hard discs in a plane, as an idealization of the scattering off a rotating target. The system displays regular or chaotic behaviour depending on the value of the only constant of motion: the Jacobi integral. We present results on the transition between regular and chaotic behaviour in terms of the periodic orbits of the system. For certain ranges of the Jacobi integral the dynamics is fully hyperbolic. The number of symbols needed to characterize the invariant set is different in each of those intervals and may become arbitrarily high. (author)
Chaotic behavior of a quantum waveguide
Energy Technology Data Exchange (ETDEWEB)
Pérez-Aguilar, H., E-mail: hiperezag@yahoo.com [Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Av. Francisco J. Mújica S/N 58030, Morelia, Michoacán (Mexico); Mendoza-Suárez, A.; Tututi, E.S. [Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Av. Francisco J. Mújica S/N 58030, Morelia, Michoacán (Mexico); Herrera-González, I.F. [Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570 Puebla (Mexico)
2013-02-15
In this work we consider an infinite quantum waveguide composed of two periodic, hard walls, one-dimensional rippled surfaces. We find that, under certain conditions, the proposed system presents some traces of quantum chaos, when the corresponding classical limit has chaotic behavior. Thus, it is possible to obtain disordered probability densities in a system with smooth surfaces. When the system has chaotic behavior we show numerically that the correlation length of the autocorrelation function of the probability density goes to zero. To corroborate some properties obtained for infinite waveguide that are physically admissible, we study the corresponding finite version of this system.
An adaptive strategy for controlling chaotic system.
Cao, Yi-Jia; Hang, Hong-Xian
2003-01-01
This paper presents an adaptive strategy for controlling chaotic systems. By employing the phase space reconstruction technique in nonlinear dynamical systems theory, the proposed strategy transforms the nonlinear system into canonical form, and employs a nonlinear observer to estimate the uncertainties and disturbances of the nonlinear system, and then establishes a state-error-like feedback law. The developed control scheme allows chaos control in spite of modeling errors and parametric variations. The effectiveness of the proposed approach has been demonstrated through its applications to two well-known chaotic systems: Duffing oscillator and Rössler chaos.
An adaptive strategy for controlling chaotic system
Institute of Scientific and Technical Information of China (English)
曹一家; 张红先
2003-01-01
This paper presents an adaptive strategy for controlling chaotic systems. By employing the phase space reconstruction technique in nonlinear dynamical systems theory, the proposed strategy transforms the nonlinear system into canonical form, and employs a nonlinear observer to estimate the uncertainties and disturbances of the nonlinear system, and then establishes a state-error-like feedback law. The developed control scheme allows chaos control in spite of modeling errors and parametric variations. The effectiveness of the proposed approach has been demonstrated through its applications to two well-known chaotic systems: Duffing oscillator and Rossler chaos.
Universal impedance fluctuations in wave chaotic systems.
Hemmady, Sameer; Zheng, Xing; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M
2005-01-14
We experimentally investigate theoretical predictions of universal impedance fluctuations in wave chaotic systems using a microwave analog of a quantum chaotic infinite square well potential. We emphasize the use of the radiation impedance to remove the nonuniversal effects of the particular coupling between the outside world and the scatterer. Specific predictions that we test include the probability density functions (PDFs) of the real and imaginary parts of the universal impedance, the equality of the variances of these PDFs, and the dependence of these PDFs on a single loss parameter.
A Design of Observers for a Discrete Chaotic System
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
It is very easy to design an observer for a discrete chaotic system which possesses one non-linear scalar quantity, and one can realize the synchronization between the investigated chaotic system and its observer easily. This method is applied to two chaotic systems.
Capability Analysis of Chaotic Mutation and Its Self-Adaption
Institute of Scientific and Technical Information of China (English)
YANG Li-Jiang; CHEN Tian-Lun
2002-01-01
Through studying several kinds of chaotic mappings' distributions of orbital points, we analyze the capabilityof the chaotic mutations based on these mappings. Nunerical experiments support our conclusions very well. Thecapability analysis also led to a self-adaptive mechanism of chaotic mutation. The introducing of the self-adaptivechaotic mutation can improve the performance of genetic algorithm very prominently.
Modeling and Chaotic Dynamics of the Laminated Composite Piezoelectric Rectangular Plate
Directory of Open Access Journals (Sweden)
Minghui Yao
2014-01-01
Full Text Available This paper investigates the multipulse heteroclinic bifurcations and chaotic dynamics of a laminated composite piezoelectric rectangular plate by using an extended Melnikov method in the resonant case. According to the von Karman type equations, Reddy’s third-order shear deformation plate theory, and Hamilton’s principle, the equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. The method of multiple scales and Galerkin’s approach are applied to the partial differential governing equation. Then, the four-dimensional averaged equation is obtained for the case of 1 : 3 internal resonance and primary parametric resonance. The extended Melnikov method is used to study the Shilnikov type multipulse heteroclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The necessary conditions of the existence for the Shilnikov type multipulse chaotic dynamics are analytically obtained. From the investigation, the geometric structure of the multipulse orbits is described in the four-dimensional phase space. Numerical simulations show that the Shilnikov type multipulse chaotic motions can occur. To sum up, both theoretical and numerical studies suggest that chaos for the Smale horseshoe sense in motion exists for the laminated composite piezoelectric rectangular plate.
Chaotic Dynamics of the Partially Follower-Loaded Elastic Double Pendulum
DEFF Research Database (Denmark)
Thomsen, Jon Juel
1995-01-01
The non-linear dynamics of the elastically restrained double pendulum, with non-conservative follower-type loading and linear damping, is re-examined with specific reference to the occurrence of chaotic motion. A local non-linear perturbation analysis is performed, showing that in three distinct ...
Super persistent chaotic transients and catastrophic bifurcation from riddled to fractal basins
Andrade, Victor Antonio
2002-01-01
This dissertation treats two related problems in chaotic dynamics: (1) super persistent chaotic transients in physical systems, and (2) catastrophic bifurcation from riddled to fractal basins. For the first problem, we investigate super persistent chaotic transient by studying the effect of noise on phase synchronization of coupled chaotic oscillators. A super persistent chaotic transient is typically induced by an unstable-unstable pair bifurcation in which two unstable periodic orbits of the same period coalesce and disappear as a system parameter is changed through a critical value. So far examples illustrating this type of transient chaos utilize discrete-time maps. We present a class of continuous-time dynamical systems that exhibit super persistent chaotic transients in parameter regimes of positive measure. In particular, we examine the effect of noise on phase synchronization of coupled chaotic oscillators. It is found that additive white noise can induce phase slips in integer multiples of 2pi's in parameter regimes where phase synchronization is expected in the absence of noise. The average time durations of the temporal phase synchronization are in fact characteristic of those of super persistent chaotic transients. We provide heuristic arguments for the scaling law of the average transient lifetime and verify it using numerical examples from both the system of coupled Chua's circuits and that of coupled Rossler oscillators. Our work suggests a way to observe super persistent chaotic transients in physically realizable systems. For the second problem, we investigate the effect of symmetry-breaking on riddling. Most existing works on riddling assume that the underlying dynamical system possesses an invariant subspace that usually results from a symmetry. In realistic applications of chaotic systems, however, there exists no perfect symmetry. The aim of this part is to examine the consequences of symmetry-breaking on riddling. In particular, we consider
Secondary chaotic terrain formation in the higher outflow channels of southern circum-Chryse, Mars
Rodriguez, J.A.P.; Kargel, J.S.; Tanaka, K.L.; Crown, D.A.; Berman, D.C.; Fairen, A.G.; Baker, V.R.; Furfaro, R.; Candelaria, P.; Sasaki, S.
2011-01-01
. Within relatively warm upper crustal materials in volcanic settings, or within highly saline crustal materials where cryopegs developed, lenses of volatiles in liquid form within the cryolithosphere could have formed, and/or remained stable.In addition, our numerical simulations suggest that low thermal conductivity, dry fine-grained porous geologic materials just a few tens of meters in thickness (e.g., dunes, sand sheets, some types of regolith materials), could have produced high thermal anomalies resulting in subsurface melting. The existence of a global layer of dry geologic materials overlying the cryolithosphere would suggest that widespread lenses of fluids existed (and may still exist) at shallow depths wherever these materials are fine-grained and porous. The surface ages of the investigated outflow channels and chaotic terrains span a full 500 to 700. Myr. Chaotic terrains similar in dimensions and morphology to secondary chaotic terrains are not observed conspicuously throughout the surface of Mars, suggesting that intra-cryolithospheric fluid lenses may form relatively stable systems. The existence of widespread groundwater lenses at shallow depths of burial has tremendous implications for exobiological studies and future human exploration. We find that the clear geomorphologic anomaly that the chaotic terrains and outflow channels of southern Chryse form within the Martian landscape could have been a consequence of large-scale resurfacing resulting from anomalously extensive subsurface melt in this region of the planet produced by high concentrations of salts within the regional upper crust. Crater count statistics reveal that secondary chaotic terrains and the outflow channels within which they occur have overlapping ages, suggesting that the instabilities leading to their formation rapidly dissipated, perhaps as the thickness of the cryolithosphere was reset following the disruption of the upper crustal thermal structure produced during outflow channel ex
Institute of Scientific and Technical Information of China (English)
WANG Jian-Gen; ZHAO Yi
2005-01-01
@@ We propose a Bang-Bang control scheme that can synchronize master-slave chaotic systems. The chaotic systems considered here are structurally different from each other. Different from some control strategies reported previously, the scheme proposed here can be taken as a generalone that is independent of the chaotic system itself.
Hybrid TS fuzzy modelling and simulation for chaotic Lorenz system
Institute of Scientific and Technical Information of China (English)
Li De-Quan
2006-01-01
The projection of the chaotic attractor observed from the Lorenz system in the X-Z plane is like a butterfly, hence the classical Lorenz system is widely known as the butterfly attractor, and has served as a prototype model for studying chaotic behaviour since it was coined. In this work we take one step further to investigate some fundamental dynamic behaviours of a novel hybrid Takagi-Sugeno (TS) fuzzy Lorenz-type system, which is essentially derived from the delta-operator-based TS fuzzy modelling for complex nonlinear systems, and contains the original Lorenz system of continuous-time TS fuzzy form as a special case. By simply and appropriately tuning the additional parametric perturbations in the two-rule hybrid TS fuzzy Lorenz-type system, complex (two-wing) butterfly attractors observed from this system in the three dimensional (3D) X-Y-Z space are created, which have not yet been reported in the literature, and the forming mechanism of the compound structures have been numerically investigated.
Chaotic motif sampler: detecting motifs from biological sequences by using chaotic neurodynamics
Matsuura, Takafumi; Ikeguchi, Tohru
Identification of a region in biological sequences, motif extraction problem (MEP) is solved in bioinformatics. However, the MEP is an NP-hard problem. Therefore, it is almost impossible to obtain an optimal solution within a reasonable time frame. To find near optimal solutions for NP-hard combinatorial optimization problems such as traveling salesman problems, quadratic assignment problems, and vehicle routing problems, chaotic search, which is one of the deterministic approaches, has been proposed and exhibits better performance than stochastic approaches. In this paper, we propose a new alignment method that employs chaotic dynamics to solve the MEPs. It is called the Chaotic Motif Sampler. We show that the performance of the Chaotic Motif Sampler is considerably better than that of the conventional methods such as the Gibbs Site Sampler and the Neighborhood Optimization for Multiple Alignment Discovery.
A Simple Chaotic Image Cryptography Algorithm Based on New Quadratic Chaotic Map
Directory of Open Access Journals (Sweden)
Saad Muhi Falih
2017-07-01
Full Text Available The chaos based cryptographic methods have been suggested some new and efficient algorithms to develop image encryption techniques because of its exceptionally desirable properties of sensitivity to initial condition and parameters of chaotic map. However, this paper proposes a new symmetric image encryption system (SIES that based on a new class of quadratic chaotic map. In this proposed scheme, the image is converted to a stream of serial bits which modulo-2 added with the stream of binary chaotic sequence generated using a new class of quadratic chaotic map. Finally, the proposed system is tested under Matlab environment and results show that the proposed technique is efficient and has high security features.
Multiplexing of discrete chaotic signals in presence of noise.
Nagaraj, Nithin; Vaidya, Prabhakar G
2009-09-01
Multiplexing of discrete chaotic signals in presence of noise is investigated. The existing methods are based on chaotic synchronization, which is susceptible to noise, precision limitations, and requires more iterates. Furthermore, most of these methods fail for multiplexing more than two discrete chaotic signals. We propose novel methods to multiplex multiple discrete chaotic signals based on the principle of symbolic sequence invariance in presence of noise and finite precision implementation of finding the initial condition of an arbitrarily long symbolic sequence of a chaotic map. Our methods work for single precision and as less as 35 iterates. For two signals, our method is robust up to 50% noise level.
Henon CSK Secure Communication System Using Chaotic Turbo Codes
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
In this paper,the authors design a novel chaotic secure communication system, which has high security and good errorcorrecting capability. Firstly, the Henon Chaos Shift Keying (CSK) modulation block is presented. Secondly,chaotic turbo encod er/decoder (hard decision) is introduced. Thirdly, this chaotic secure communication system, which comprises the Henon CSK modulation block and chaotic turbo en coder in a serially concatenated form, is shown. Furthermore, a novel two step encryption scheme is proposed, which is based on the chaotic turbo e ncoded Henon CSK secure communication system.
New robust chaotic system with exponential quadratic term
Institute of Scientific and Technical Information of China (English)
Bao Bo-Cheng; Li Chun-Biao; Xu Jian-Peing; Liu Zhong
2008-01-01
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term.This system can display a double-scroll chaotic attractor with only two equilibria,and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent.Some basic dynamical properties and chaotic behaviour of novel attractor are studied.By numerical simulation,this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviottrs by a constant controller.
Target Detection and Ranging through Lossy Media using Chaotic Radar
Directory of Open Access Journals (Sweden)
Bingjie Wang
2015-04-01
Full Text Available A chaotic radar system has been developed for through-wall detection and ranging of targets. The chaotic signal generated by an improved Colpitts oscillator is designed as a probe signal. Ranging to target is achieved by the cross-correlation between the time-delayed reflected return signal and the replica of the transmitted chaotic signal. In this paper, we explore the performance of the chaotic radar system for target detection and ranging through lossy media. Experimental results show that the designed chaotic radar has the advantages of high range resolution, unambiguous correlation profile, and can be used for through wall target detection and sensing.
Cascade adaptive control of uncertain unified chaotic systems
Institute of Scientific and Technical Information of China (English)
Wei Wei; Li Dong-Hai; Wang Jing
2011-01-01
The chaos control of uncertain unified chaotic systems is considered. Cascade adaptive control approach with only one control input is presented to stabilize states of the uncertain unified chaotic system at the zero equilibrium point.Since an adaptive controller based on dynamic compensation mechanism is employed, the exact model of the unified chaotic system is not necessarily required.By choosing appropriate controller parameters, chaotic phenomenon can be suppressed and the response speed is tunable. Sufficient condition for the asymptotic stability of the approach is derived. Numerical simulation results confirm that the cascade adaptive control approach with only one control signal is valid in chaos control of uncertain unified chaotic systems.
Design of Threshold Controller Based Chaotic Circuits
DEFF Research Database (Denmark)
Mohamed, I. Raja; Murali, K.; Sinha, Sudeshna
2010-01-01
We propose a very simple implementation of a second-order nonautonomous chaotic oscillator, using a threshold controller as the only source of nonlinearity. We demonstrate the efficacy and simplicity of our design through numerical and experimental results. Further, we show that this approach of ...
Chaotic behaviour of photonic crystals resonators
Di Falco, A.
2015-02-08
We show here theoretically and experimentally how chaotic Photonic Crystal resonators can be used for en- ergy harvesting applications and the demonstration of fundamental theories, like the onset of superradiance in quantum systems. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Quantum noise-induced chaotic oscillations
Bag, Bidhan Chandra; Ray, Deb Shankar
1999-01-01
We examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxiliary Hamiltonian manifests itself as an additional fluctuational degree of freedom which may induce chaotic and regular oscillations in a nonlinear oscillator.
Quantum noise-induced chaotic oscillations
Bag, B C; Bag, Bidhan Chandra; Ray, Deb Shankar
1999-01-01
We examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxilliary Hamiltonian manifests itself as an additional fluctuational degree of freedom which may induce chaotic and regular oscillations in a nonlinear oscillator.
Correlation Widths in Quantum--Chaotic Scattering
Dietz, B.; Richter, A; WeidenmÜller, H.
2011-01-01
An important parameter to characterize the scattering matrix S for quantum-chaotic scattering is the width Gamma_{corr} of the S-matrix autocorrelation function. We show that the "Weisskopf estimate" d/(2pi) sum_c T_c (where d is the mean resonance spacing, T_c with 0
Chaotic instantons in scalar field theory
Addazi, Andrea
2016-01-01
We consider a new class of instantons in context of quantum field theory of a scalar field coupled with a chaotic background source field. We show how the instanton associated to the quantum tunneling from a metastable false to the true vacuum will be corrected by an exponential enhancement factor. Possible implications are discussed.
Impulsive generalized synchronization of chaotic system
Institute of Scientific and Technical Information of China (English)
Zhang Rong; Xu Zhen-Yuan; He Xue-Ming
2007-01-01
In this paper, with a given manifold y=H(x), we have constructed a response system for a continuous-time chaotic system as a drive system, and used impulsive control theory to demonstrate theoretically that this response system can achieve impulsive generalized synchronization(GS)with the drive system. Our theoretical result is supported by numerical examples.
Generalized synchronization of two different chaotic systems
Institute of Scientific and Technical Information of China (English)
Li Guo-Hui
2007-01-01
In this paper, generalized synchronization of two different chaotic dynamical systems is investigated. An active control is adopted to construct a response system which synchronizes with a given drive system for a function relation.Based on rigorous analysis, the error system is asymptotically stable at the equilibrium. Numerical simulations illustrate the effectiveness of the proposed theory.
Chaotic behavior of a layered neural network
Energy Technology Data Exchange (ETDEWEB)
Derrida, B.; Meir, R.
1988-09-15
We consider the evolution of configurations in a layered feed-forward neural network. Exact expressions for the evolution of the distance between two configurations are obtained in the thermodynamic limit. Our results show that the distance between two arbitrarily close configurations always increases, implying chaotic behavior, even in the phase of good retrieval.
Phase multistability of synchronous chaotic oscillations
Directory of Open Access Journals (Sweden)
T. E. Vadivasova
2000-01-01
Full Text Available The paper describes the sequence of bifurcations leading to multistability of periodic and chaotic synchronous attractors for the coupled Rössler systems which individually demonstrate the Feigenbaum route to chaos. We investigate how a frequency mismatch affects this phenomenon. The role of a set of coexisting synchronous regimes in the transitions to and between different forms of synchronization is studied.
Robust synchronization of uncertain chaotic systems
Institute of Scientific and Technical Information of China (English)
Li Fang; Hu Ai-Hua; Xu Zheng-Yuan
2006-01-01
This paper investigates robust unified (lag, anticipated, and complete) synchronization of two coupled chaotic systems. By introducing the concepts of positive definite symmetrical matrix and Riccati inequality and the theory of robust stability, several criteria on robust synchronization are established. Extensive numerical simulations are also used to confirm the results.
Formulation of statistical mechanics for chaotic systems
Indian Academy of Sciences (India)
Vishnu M Bannur; Ramesh Babu Thayyullathil
2009-02-01
We formulate the statistical mechanics of chaotic system with few degrees of freedom and investigated the quartic oscillator system using microcanonical and canonical ensembles. Results of statistical mechanics are numerically verified by considering the dynamical evolution of quartic oscillator system with two degrees of freedom.
Learning chaotic attractors by neural networks
Bakker, R; Schouten, JC; Giles, CL; Takens, F; van den Bleek, CM
2000-01-01
An algorithm is introduced that trains a neural network to identify chaotic dynamics from a single measured time series. During training, the algorithm learns to short-term predict the time series. At the same time a criterion, developed by Diks, van Zwet, Takens, and de Goede (1996) is monitored th
Application of Chaotic Number Generators in Econophysics
Pellicer-Lostao, Carmen
2011-01-01
Agent-based models have demonstrated their power and flexibility in Econophysics. However their major challenge is still to devise more realistic simulation scenarios. The complexity of Economy makes appealing the idea of introducing chaotic number generators as simulation engines in these models. Chaos based number generators are easy to use and highly configurable. This makes them just perfect for this application.
Performance analysis of chaotic and white watermarks in the presence of common watermark attacks
Energy Technology Data Exchange (ETDEWEB)
Mooney, Aidan [Department of Computer Science, NUI Maynooth, Co. Kildare (Ireland)], E-mail: amooney@cs.nuim.ie; Keating, John G. [Department of Computer Science, NUI Maynooth, Co. Kildare (Ireland)], E-mail: john.keating@nuim.ie; Heffernan, Daniel M. [Department of Mathematical Physics, NUI Maynooth, Co. Kildare (Ireland); School of Theoretical Physics, Dublin Institute for Advanced Studies, Dublin 4 (Ireland)], E-mail: dmh@thphys.nuim.ie
2009-10-15
Digital watermarking is a technique that aims to embed a piece of information permanently into some digital media, which may be used at a later stage to prove owner authentication and attempt to provide protection to documents. The most common watermark types used to date are pseudorandom number sequences which possess a white spectrum. Chaotic watermark sequences have been receiving increasing interest recently and have been shown to be an alternative to the pseudorandom watermark types. In this paper the performance of pseudorandom watermarks and chaotic watermarks in the presence of common watermark attacks is performed. The chaotic watermarks are generated from the iteration of the skew tent map, the Bernoulli map and the logistic map. The analysis focuses on the watermarked images after they have been subjected to common image distortion attacks. The capacities of each of these images are also calculated. It is shown that signals generated from lowpass chaotic signals have superior performance over the other signal types analysed for the attacks studied.
Building Chaotic Model From Incomplete Time Series
Siek, Michael; Solomatine, Dimitri
2010-05-01
This paper presents a number of novel techniques for building a predictive chaotic model from incomplete time series. A predictive chaotic model is built by reconstructing the time-delayed phase space from observed time series and the prediction is made by a global model or adaptive local models based on the dynamical neighbors found in the reconstructed phase space. In general, the building of any data-driven models depends on the completeness and quality of the data itself. However, the completeness of the data availability can not always be guaranteed since the measurement or data transmission is intermittently not working properly due to some reasons. We propose two main solutions dealing with incomplete time series: using imputing and non-imputing methods. For imputing methods, we utilized the interpolation methods (weighted sum of linear interpolations, Bayesian principle component analysis and cubic spline interpolation) and predictive models (neural network, kernel machine, chaotic model) for estimating the missing values. After imputing the missing values, the phase space reconstruction and chaotic model prediction are executed as a standard procedure. For non-imputing methods, we reconstructed the time-delayed phase space from observed time series with missing values. This reconstruction results in non-continuous trajectories. However, the local model prediction can still be made from the other dynamical neighbors reconstructed from non-missing values. We implemented and tested these methods to construct a chaotic model for predicting storm surges at Hoek van Holland as the entrance of Rotterdam Port. The hourly surge time series is available for duration of 1990-1996. For measuring the performance of the proposed methods, a synthetic time series with missing values generated by a particular random variable to the original (complete) time series is utilized. There exist two main performance measures used in this work: (1) error measures between the actual
Chaotic Map Construction from Common Nonlinearities and Microcontroller Implementations
Ablay, Günyaz
2016-06-01
This work presents novel discrete-time chaotic systems with some known physical system nonlinearities. Dynamic behaviors of the models are examined with numerical methods and Arduino microcontroller-based experimental studies. Many new chaotic maps are generated in the form of x(k + 1) = rx(k) + f(x(k)) and high-dimensional chaotic systems are obtained by weak coupling or cross-coupling the same or different chaotic maps. An application of the chaotic maps is realized with Arduino for chaotic pulse width modulation to drive electrical machines. It is expected that the new chaotic maps and their microcontroller implementations will facilitate practical chaos-based applications in different fields.
Applications of chaotic neurodynamics in pattern recognition
Baird, Bill; Freeman, Walter J.; Eeckman, Frank H.; Yao, Yong
1991-08-01
Network algorithms and architectures for pattern recognition derived from neural models of the olfactory system are reviewed. These span a range from highly abstract to physiologically detailed, and employ the kind of dynamical complexity observed in olfactory cortex, ranging from oscillation to chaos. A simple architecture and algorithm for analytically guaranteed associative memory storage of analog patterns, continuous sequences, and chaotic attractors in the same network is described. A matrix inversion determines network weights, given prototype patterns to be stored. There are N units of capacity in an N node network with 3N2 weights. It costs one unit per static attractor, two per Fourier component of each sequence, and three to four per chaotic attractor. There are no spurious attractors, and for sequences there is a Liapunov function in a special coordinate system which governs the approach of transient states to stored trajectories. Unsupervised or supervised incremental learning algorithms for pattern classification, such as competitive learning or bootstrap Widrow-Hoff can easily be implemented. The architecture can be ''folded'' into a recurrent network with higher order weights that can be used as a model of cortex that stores oscillatory and chaotic attractors by a Hebb rule. Network performance is demonstrated by application to the problem of real-time handwritten digit recognition. An effective system with on-line learning has been written by Eeckman and Baird for the Macintosh. It utilizes static, oscillatory, and/or chaotic attractors of two kinds--Lorenze attractors, or attractors resulting from chaotically interacting oscillatory modes. The successful application to an industrial pattern recognition problem of a network architecture of considerable physiological and dynamical complexity, developed by Freeman and Yao, is described. The data sets of the problem come in three classes of difficulty, and performance of the biological network is
Chaotic Attractor Crisis and Climate Sensitivity: a Transfer Operator Approach
Tantet, A.; Lucarini, V.; Lunkeit, F.; Dijkstra, H. A.
2015-12-01
The rough response to a smooth parameter change of some non-chaotic climate models, such as the warm to snowball-Earth transition in energy balance models due to the ice-albedo feedback, can be studied in the framework of bifurcation theory, in particular by analysing the Lyapunov spectrum of fixed points or periodic orbits. However, bifurcation theory is of little help to study the destruction of a chaotic attractor which can occur in high-dimensional General Circulation Models (GCM). Yet, one would expect critical slowing down to occur before the crisis, since, as the system becomes susceptible to the physical instability mechanism responsible for the crisis, it turns out to be less and less resilient to exogenous perturbations and to spontaneous fluctuations due to other types of instabilities on the attractor. The statistical physics framework, extended to nonequilibrium systems, is particularly well suited for the study of global properties of chaotic and stochastic systems. In particular, the semigroup of transfer operators governs the evolution of distributions in phase space and its spectrum characterises both the relaxation rate of distributions to a statistical steady-state and the stability of this steady-state to perturbations. If critical slowing down indeed occurs in the approach to an attractor crisis, the gap in the spectrum of the semigroup of transfer operators is expected to shrink. We show that the chaotic attractor crisis due to the ice-albedo feedback and resulting in a transition from a warm to a snowball-Earth in the Planet Simulator (PlaSim), a GCM of intermediate complexity, is associated with critical slowing down, as observed by the slower decay of correlations before the crisis (cf. left panel). In addition, we demonstrate that this critical slowing down can be traced back to the shrinkage of the gap between the leading eigenvalues of coarse-grained approximations of the transfer operators and that these eigenvalues capture the
Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing
Kumar, Suhas; Strachan, John Paul; Williams, R. Stanley
2017-08-01
At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos, and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking. Here we describe niobium dioxide (NbO2) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal-insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator and observe a tunable range of periodic and chaotic self-oscillations. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such
Directory of Open Access Journals (Sweden)
Hanzhong Zheng
2014-01-01
Full Text Available A systematic methodology is developed for multi-images encryption and decryption and field programmable gate array (FPGA embedded implementation by using single discrete time chaotic system. To overcome the traditional limitations that a chaotic system can only encrypt or decrypt one image, this paper initiates a new approach to design n-dimensional (n-D discrete time chaotic controlled systems via some variables anticontrol, which can achieve multipath drive-response synchronization. To that end, the designed n-dimensional discrete time chaotic controlled systems are used for multi-images encryption and decryption. A generalized design principle and the corresponding implementation steps are also given. Based on the FPGA embedded hardware system working platform with XUP Virtex-II type, a chaotic secure communication system for three digital color images encryption and decryption by using a 7D discrete time chaotic system is designed, and the related system design and hardware implementation results are demonstrated, with the related mathematical problems analyzed.
Origin of the chaotic motion of the Saturnian satellite Atlas
Renner, S; Moutamid, M El; Sicardy, B; Vienne, A; Murray, C D; Saillenfest, M
2016-01-01
We revisit the dynamics of Atlas. Using Cassini ISS astrometric observations spanning February 2004 to August 2013, Cooper et al. (2015) found evidence that Atlas is currently perturbed by both a 54:53 corotation eccentricity resonance (CER) and a 54:53 Lindblad eccentricity resonance (LER) with Prometheus. They demonstrated that the orbit of Atlas is chaotic, with a Lyapunov time of order 10 years, as a direct consequence of the coupled resonant interaction (CER/LER) with Prometheus. Here we investigate the interactions between the two resonances using the CoraLin analytical model (El Moutamid et al. 2014), showing that the chaotic zone fills almost all the corotation sites occupied by the satellite's orbit. Four 70:67 apse-type mean motion resonances with Pandora are also overlapping, but these resonances have a much weaker effect. Frequency analysis allows us to highlight the coupling between the 54:53 resonances, and confirms that a simplified system including the perturbations due to Prometheus and Satur...
Cross-section fluctuations in chaotic scattering systems
Ericson, Torleif E. O.; Dietz, Barbara; Richter, Achim
2016-10-01
Exact analytical expressions for the cross-section correlation functions of chaotic scattering systems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are applicable beyond these restrictions. The derivation is based on a statistical model of Breit-Wigner type for chaotic scattering amplitudes which has been shown to describe the exact analytical results for the scattering (S )-matrix correlation functions accurately. Our results are given in the energy and in the time representations and apply in the whole range from isolated to overlapping resonances. The S -matrix contributions to the cross-section correlations are obtained in terms of explicit irreducible and reducible correlation functions. Consequently, the model can be used for a detailed exploration of the key features of the cross-section correlations and the underlying physical mechanisms. In the region of isolated resonances, the cross-section correlations contain a dominant contribution from the self-correlation term. For narrow states the self-correlations originate predominantly from widely spaced states with exceptionally large partial width. In the asymptotic region of well-overlapping resonances, the cross-section autocorrelation functions are given in terms of the S -matrix autocorrelation functions. For inelastic correlations, in particular, the Ericson fluctuations rapidly dominate in that region. Agreement with known analytical and experimental results is excellent.
A chaotic system with a single unstable node
Energy Technology Data Exchange (ETDEWEB)
Sprott, J.C. [Department of Physics, University of Wisconsin, Madison, WI 53706 (United States); Jafari, Sajad, E-mail: sajadjafari@aut.ac.ir [Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413 (Iran, Islamic Republic of); Pham, Viet-Thanh [School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi (Viet Nam); Hosseini, Zahra Sadat [Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413 (Iran, Islamic Republic of)
2015-09-25
This paper describes an unusual example of a three-dimensional dissipative chaotic flow with quadratic nonlinearities in which the only equilibrium is an unstable node. The region of parameter space with bounded solutions is relatively small as is the basin of attraction, which accounts for the difficulty of its discovery. Furthermore, for some values of the parameters, the system has an attracting torus, which is uncommon in three-dimensional systems, and this torus can coexist with a strange attractor or with a limit cycle. The limit cycle and strange attractor exhibit symmetry breaking and attractor merging. All the attractors appear to be hidden in that they cannot be found by starting with initial conditions in the vicinity of the equilibrium, and thus they represent a new type of hidden attractor with important and potentially problematic engineering consequences. - Highlights: • An unusual example of a three-dimensional dissipative chaotic flow is introduced. • In this system the only equilibrium is an unstable node. • For some values of the parameters, the system has an attracting torus. • This torus can coexist with a strange attractor or with a limit cycle. • These properties are uncommon in three-dimensional systems.
Origin of the Chaotic Motion of the Saturnian Satellite Atlas
Renner, S.; Cooper, N. J.; El Moutamid, M.; Sicardy, B.; Vienne, A.; Murray, C. D.; Saillenfest, M.
2016-05-01
We revisit the dynamics of Atlas. Using Cassini ISS astrometric observations spanning 2004 February to 2013 August, Cooper et al. found evidence that Atlas is currently perturbed by both a 54:53 corotation eccentricity resonance (CER) and a 54:53 Lindblad eccentricity resonance (LER) with Prometheus. They demonstrated that the orbit of Atlas is chaotic, with a Lyapunov time of order 10 years, as a direct consequence of the coupled resonant interaction (CER/LER) with Prometheus. Here we investigate the interactions between the two resonances using the CoraLin analytical model, showing that the chaotic zone fills almost all the corotation sites occupied by the satellite's orbit. Four 70:67 apse-type mean motion resonances with Pandora are also overlapping, but these resonances have a much weaker effect. Frequency analysis allows us to highlight the coupling between the 54:53 resonances, and confirms that a simplified system including the perturbations due to Prometheus and Saturn's oblateness only captures the essential features of the dynamics.
High-dimensional chaotic and attractor systems a comprehensive introduction
Ivancevic, Vladimir G
2007-01-01
This is a graduate–level monographic textbook devoted to understanding, prediction and control of high–dimensional chaotic and attractor systems of real life. The objective of the book is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high–dimensional chaotic and attractor dynamics. The book has nine Chapters. The first Chapter gives a textbook-like introduction into the low-dimensional attractors and chaos. This Chapter has an inspirational character, similar to other books on nonlinear dynamics and deterministic chaos. The second Chapter deals with Smale’s topological transformations of stretching, squeezing and folding (of the system’s phase–space), developed for the purpose of chaos theory. The third Chapter is devoted to Poincaré's 3-body problem and basic techniques of chaos control, mostly of Ott-Grebogi-Yorke type. The fourth Chapter is a review of both Landau’s and topological phase transition theory, as w...
Binary black hole shadows, chaotic scattering and the Cantor set
Shipley, Jake
2016-01-01
We investigate the qualitative features of binary black hole shadows using the model of two extremally charged black holes in static equilibrium (a Majumdar--Papapetrou solution). Our perspective is that binary spacetimes are natural exemplars of {\\it chaotic scattering}, because they admit more than one fundamental null orbit, and thus an uncountably-infinite set of perpetual orbits which generate scattering singularities in initial data. Inspired by the three-disc model, we develop an appropriate symbolic dynamics to describe planar null geodesics on the double black hole spacetime. We show that a one-dimensional (1D) black hole shadow may constructed through an iterative procedure akin to the construction of the Cantor set; thus the shadow is self-similar. Next, we study non-planar rays, to understand how angular momentum affects the existence and properties of the fundamental null orbits. Taking slices through 2D shadows, we observe three types of 1D shadow: regular, Cantor-like, and highly chaotic. The s...
Virtual Libraries: Interactive Support Software and an Application in Chaotic Models.
Katsirikou, Anthi; Skiadas, Christos; Apostolou, Apostolos; Rompogiannakis, Giannis
This paper begins with a discussion of the characteristics and the singularity of chaotic systems, including dynamic systems theory, chaotic orbit, fractals, chaotic attractors, and characteristics of chaotic systems. The second section addresses the digital libraries (DL) concept and the appropriateness of chaotic models, including definition and…
Enhanced energy storage in chaotic optical resonators
Liu, Changxu
2013-05-05
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability, which makes it difficult to predict or explain experimental results. Conversely, we demonstrate here how chaos can be used to enhance the ability of an optical resonator to store energy. We combine analytic theory with ab initio simulations and experiments in photonic-crystal resonators to show that a chaotic resonator can store six times more energy than its classical counterpart of the same volume. We explain the observed increase by considering the equipartition of energy among all degrees of freedom of the chaotic resonator (that is, the cavity modes) and discover a convergence of their lifetimes towards a single value. A compelling illustration of the theory is provided by enhanced absorption in deformed polystyrene microspheres. © 2013 Macmillan Publishers Limited. All rights reserved.
Delusions, superstitious conditioning and chaotic dopamine neurodynamics.
Shaner, A
1999-02-01
Excessive mesolimbic dopaminergic neurotransmission is closely related to the psychotic symptoms of schizophrenia. A mathematical model of dopamine neuron firing rates, developed by King and others, suggests a mechanism by which excessive dopaminergic transmission could produce psychotic symptoms, especially delusions. In this model, firing rates varied chaotically when the efficacy of dopaminergic transmission was enhanced. Such non-contingent changes in firing rates in mesolimbic reward pathways could produce delusions by distorting thinking in the same way that non-contingent reinforcement produces superstitious conditioning. Though difficult to test in humans, the hypothesis is testable as an explanation for a common animal model of psychosis--amphetamine stereotypy in rats. The hypothesis predicts that: (1) amphetamine will cause chaotic firing rates in mesolimbic dopamine neurons; (2) non-contingent brain stimulation reward will produce stereotypy; (3) non-contingent microdialysis of dopamine into reward areas will produce stereotypy; and (4) dopamine antagonists will block all three effects.
Revisiting the minimal chaotic inflation model
Energy Technology Data Exchange (ETDEWEB)
Harigaya, Keisuke, E-mail: keisukeharigaya@berkeley.edu [ICRR, University of Tokyo, Kashiwa, Chiba 277-8582 (Japan); Ibe, Masahiro; Kawasaki, Masahiro [ICRR, University of Tokyo, Kashiwa, Chiba 277-8582 (Japan); Kavli IPMU (WPI), UTIAS, University of Tokyo, Kashiwa, Chiba 277-8583 (Japan); Yanagida, Tsutomu T. [Kavli IPMU (WPI), UTIAS, University of Tokyo, Kashiwa, Chiba 277-8583 (Japan)
2016-05-10
We point out that the prediction of the minimal chaotic inflation model is altered if a scalar field takes a large field value close to the Planck scale during inflation due to a negative Hubble induced mass. In particular, we show that the inflaton potential is effectively flattened at a large inflaton field value in the presence of such a scalar field. The scalar field may be identified with the standard model Higgs field or super partners of standard model fermions. With such Hubble-induced flattening, we find that the minimal chaotic inflation model, especially the model with a quadratic potential, is consistent with recent observations of the cosmic microwave background fluctuation without modifying the inflation model itself.
Chaotic desynchronization of multi-strain diseases
Schwartz, I B; Cummings, D A T; Billings, L; McCrary, M; Burke, D S; Schwartz, Ira B.; Shaw, Leah B.; Cummings, Derek A. T.; Billings, Lora; Crary, Marie Mc; Burke, Donald S.
2005-01-01
Multi-strain diseases are diseases that consist of several strains, or serotypes. The serotypes may interact by antibody-dependent enhancement (ADE), in which infection with a single serotype is asymptomatic, but infection with a second serotype leads to serious illness accompanied by greater infectivity. It has been observed from serotype data of dengue hemorrhagic fever that outbreaks of the four serotypes occur asynchronously. Both autonomous and seasonally driven outbreaks were studied in a model containing ADE. For sufficiently small ADE, the number of infectives of each serotype synchronizes, with outbreaks occurring in phase. When the ADE increases past a threshold, the system becomes chaotic, and infectives of each serotype desynchronize. However, certain groupings of the primary and second ary infectives remain synchronized even in the chaotic regime.
Chaotic Discrimination and Non-Linear Dynamics
Directory of Open Access Journals (Sweden)
Partha Gangopadhyay
2005-01-01
Full Text Available This study examines a particular form of price discrimination, known as chaotic discrimination, which has the following features: sellers quote a common price but, in reality, they engage in secret and apparently unsystematic price discounts. It is widely held that such forms of price discrimination are seriously inconsistent with profit maximization by sellers.. However, there is no theoretical salience to support this kind of price discrimination. By straining the logic of non-linear dynamics this study explains why such secret discounts are chaotic in the sense that sellers fail to adopt profit-maximising price discounts. A model is developed to argue that such forms of discrimination may derive from the regions of instability of a dynamic model of price discounts.
Communicating via robust synchronization of chaotic lasers
Energy Technology Data Exchange (ETDEWEB)
Lopez-Gutierrez, R.M. [Engineering Faculty, Baja California Autonomous University (UABC), Km. 103 Carret. Tij-Ens., 22860 Ensenada, B.C. (Mexico); Posadas-Castillo, C. [Engineering Faculty, Baja California Autonomous University (UABC), Km. 103 Carret. Tij-Ens., 22860 Ensenada, B.C. (Mexico); FIME, Autonomous University of Nuevo Leon (UANL), Pedro de Alba, S.N., Cd. Universitaria, San Nicolas de los Garza, NL (Mexico); Lopez-Mancilla, D. [Departamento de Ciencias Exactas y Tecnologicas, Centro Universitario de los Lagos, Universidad de Guadalajara (CULagos-UdeG), Enrique Diaz de Leon s/n, 47460 Lagos de Moreno, Jal. (Mexico); Cruz-Hernandez, C. [Electronics and Telecommunications Department, Scientific Research and Advanced Studies of Ensenada (CICESE), Km. 107 Carret. Tij-Ens., 22860 Ensenada, B.C. (Mexico)], E-mail: ccruz@cicese.mx
2009-10-15
In this paper, the robust synchronization problem for coupled chaotic Nd:YAG lasers is addressed. We resort to complex systems theory to achieve chaos synchronization. Based on stability theory, it is shown that the state trajectories of the perturbed error synchronization are ultimately bounded, provided the unperturbed synchronization error system is exponentially stable, and some conditions on the bounds of the perturbation terms are satisfied. So that, encoding, transmission, and decoding in chaotic optical communications are presented. We analyze the transmission and recovery of encrypted information when parameter mismatches are considered. Computer simulations are provided to show the effectiveness of this robustness synchronization property, we present the encrypted transmission of image messages, and we show that, the transmitted image is faithfully recovered.
Control of partial synchronization in chaotic oscillators
Indian Academy of Sciences (India)
R Banerjee; E Padmanaban; S K Dana
2015-02-01
A design of coupling is proposed to control partial synchronization in two chaotic oscillators in a driver–response mode. A control of synchrony between one response variables is made possible (a transition from a complete synchronization to antisynchronization via amplitude death and vice versa without loss of synchrony) keeping the other pairs of variables undisturbed in their pre-desired states of coherence. Further, one of the response variables can be controlled so as to follow the dynamics of an external signal (periodic or chaotic) while keeping the coherent status of other variables unchanged. The stability of synchronization is established using the Hurwitz matrix criterion. Numerical example of an ecological foodweb model is presented. The control scheme is demonstrated in an electronic circuit of the Sprott system.
Gas lasers with wave-chaotic resonators
Zaitsev, Oleg
2010-01-01
Semiclassical multimode laser theory is extended to gas lasers with open two-dimensional resonators of arbitrary shape. The Doppler frequency shift of the linear-gain coefficient leads to an additional linear coupling between the modes, which, however, is shown to be negligible. The nonlinear laser equations simplify in the special case of wave-chaotic resonators. In the single-mode regime, the intensity of a chaotic laser, as a function of the mode frequency, displays a local minimum at the frequency of the atomic transition. The width of the minimum scales with the inhomogeneous linewidth, in contrast to the Lamb dip in uniaxial resonators whose width is given by the homogeneous linewidth.
Entanglement production in Quantized Chaotic Systems
Bandyopadhyay, J N; Bandyopadhyay, Jayendra N.; Lakshminarayan, Arul
2005-01-01
Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical studies. We find that, in general, presence of chaos in the system produces more entanglement. However, coupling strength between two subsystems is also very important parameter for the entanglement production. Here we show how chaos can lead to large entanglement which is universal and describable by random matrix theory (RMT). We also explain entanglement production in coupled strongly chaotic systems by deriving a formula based on RMT. This formula is valid for arbitrary coupling strengths, as well as for sufficiently long time. Here we investigate also the effect of chaos on the entanglement production for the mixed initial state. We find that many properties of the mixed state entanglement production...
Fractal dynamics in chaotic quantum transport.
Kotimäki, V; Räsänen, E; Hennig, H; Heller, E J
2013-08-01
Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis-a widely used method in time-series analysis-and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.
Quantum chaotic dynamics and random polynomials
Energy Technology Data Exchange (ETDEWEB)
Bogomolny, E.; Bohigas, O.; Leboeuf, P.
1995-11-01
The distribution of roots of polynomials of high degree with random coefficients is investigated which, among others, appear naturally in the context of `quantum chaotic dynamics`. It is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plane. In order to further increase this tendency, the particular case of self-inverse random polynomials is studied, and it is shown that for them a finite portion of all roots lies exactly on the unit circle. Correlation functions of these roots are also computed analytically, and compared to the correlations of eigenvalues of random matrices. The problem of ergodicity of chaotic wavefunctions is also considered. Special attention is devoted to the role of symmetries in the distribution of roots of random polynomials. (author). 32 refs.
Bearing Health Assessment Based on Chaotic Characteristics
Directory of Open Access Journals (Sweden)
Chen Lu
2013-01-01
Full Text Available Vibration signals extracted from rotating parts of machinery carry a lot of useful information about the condition of operating machine. Due to the strong non-linear, complex and non-stationary characteristics of vibration signals from working bearings, an accurate and reliable health assessment method for bearing is necessary. This paper proposes to utilize the selected chaotic characteristics of vibration signal for health assessment of a bearing by using self-organizing map (SOM. Both Grassberger-Procaccia algorithm and Takens' theory are employed to calculate the characteristic vector which includes three chaotic characteristics, such as correlation dimension, largest Lyapunov exponent and Kolmogorov entropy. After that, SOM is used to map the three corresponding characteristics into a confidence value (CV which represents the health state of the bearing. Finally, a case study based on vibration datasets of a group of testing bearings was conducted to demonstrate that the proposed method can reliably assess the health state of bearing.
The Mixmaster universe A chaotic Farey tale
Cornish, N; Cornish, Neil; Levin, Janna
1997-01-01
When gravitational fields are at their strongest, the evolution of spacetime is thought to be highly erratic. Over the past decade debate has raged over whether this evolution can be classified as chaotic. The debate has centered on the homogeneous but anisotropic mixmaster universe. A definite resolution has been lacking as the techniques used to study the mixmaster dynamics yield observer dependent answers. Here we resolve the conflict by using observer independent, fractal methods. We prove the mixmaster universe is chaotic by exposing the fractal strange repellor that characterizes the dynamics. The repellor is laid bare in both the 6-dimensional minisuperspace of the full Einstein equations, and in a 2-dimensional discretisation of the dynamics. The chaos is encoded in a special set of numbers that form the irrational Farey tree. We quantify the chaos by calculating the strange repellor's Lyapunov dimension, topological entropy and multifractal dimensions. As all of these quantities are coordinate, or ga...
A Chaotic Approach to Market Dynamics
Pellicer-Lostao, Carmen
2010-01-01
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics is offering models of markets as complex systems, such as the gas-like model, able to predict money distributions observed in real economies. However, this model reveals some technical hitches to explain the power law (Pareto) distribution, observed in individuals with high incomes. Here, non linear dynamics is introduced in the gas-like model. The results obtained demonstrate that a chaotic gas-like model can reproduce the two money distributions observed in real economies (Exponential and Pareto). Moreover, it is able to control the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear in the market and doom it to complete inequality.
Reversibility, coarse graining and the chaoticity principle
Bonetto, F
1997-01-01
We describe a way of interpreting the chaotic principle of (ref. [GC1]) more extensively than it was meant in the original works. Mathematically the analysis is based on the dynamical notions of Axiom A and Axiom B and on the notion of Axiom C, that we introduce arguing that it is suggested by the results of an experiment (ref. [BGG]) on chaotic motions. Physically we interpret a breakdown of the Anosov property of a time reversible attractor (replaced, as a control parameter changes, by an Axiom A property) as a spontaneous breakdown of the time reversal symmetry: the relation between time reversal and the symmetry that remains after the breakdown is analogous to the breakdown of T-invariance while TCP still holds.
Spice Modeling of the Vilnius Chaotic Oscillator
Peters, R D
2005-01-01
``A simple chaotic oscillator for educational purposes'' was recently described in the literature [1]. In addition to their hardware description, the authors of this paper generated a bifurcation diagram from the model equations presented in their paper. In the present treatment of their circuit the `simulation program for integrated circuit engineering' (Spice) has been used to generate some insightful graphs that were not shown by the Lithuania group.
Quantum chaotic attractor in a dissipative system
Liu, W V; Schieve, William C.
1997-01-01
A dissipative quantum system is treated here by coupling it with a heat bath of harmonic oscillators. Through quantum Langevin equations and Ehrenfest's theorem, we establish explicitly the quantum Duffing equations with a double-well potential chosen. A quantum noise term appears the only driving force in dynamics. Numerical studies show that the chaotic attractor exists in this system while chaos is certainly forbidden in the classical counterpart.
Spin-torsion in Chaotic Inflation
Garcia de Andrade, L C
1999-01-01
The role of spin-torsion coupling to gravity is analyzed in the context of a model of chaotic inflation. The system of equations constructed from the Einstein-Cartan and inflaton field equations are studied and it is shown that spin-torsion interactions are effective only at the very first e-folds of inflation, becoming quickly negligible and, therefore, not affecting the standard inflationary scenario nor the density perturbations spectrum predictions.
Nonuniversality of weak synchronization in chaotic systems
Vieira, M. de Sousa; Lichtenberg, A.J.
1997-01-01
We show that the separate properties of weak synchronization (WS) and strong synchronization (SS), reported recently by Pyragas [K. Pyragas, Phys. Rev. E, 54, R4508 (1996)], in unidirectionally coupled chaotic systems, are not generally distinct properties of such systems. In particular, we find analytically for the tent map and numerically for some parameters of the circle map that the transition to WS and SS coincide.
On chaotic conductivity in the magnetotail
Holland, Daniel L.; Chen, James
1992-01-01
The concept of chaotic conductivity and the acceleration of particles due to a constant dawn dusk electric field are studied in a magnetotail-like magnetic field. A test particle simulation is used including the full nonlinear dynamics. It is found that the acceleration process can be understood without invoking chaos and that the cross tail current is determined by the particle dynamics and distributions. It is concluded that in general there is no simple relationship between the electric field and the current.
Chaotic ion motion in magnetosonic plasma waves
Varvoglis, H.
1984-01-01
The motion of test ions in a magnetosonic plasma wave is considered, and the 'stochasticity threshold' of the wave's amplitude for the onset of chaotic motion is estimated. It is shown that for wave amplitudes above the stochasticity threshold, the evolution of an ion distribution can be described by a diffusion equation with a diffusion coefficient D approximately equal to 1/v. Possible applications of this process to ion acceleration in flares and ion beam thermalization are discussed.
Chaotic Phenomena in Technical Control Systems
DEFF Research Database (Denmark)
Mosekilde, Erik
1997-01-01
The paper discusses a number of examples of technical control systems that can exhibit deterministic chaos and other forms of complex nonlinear behavior. These examples include thermostatically regulated radiators, closely placed refrigirators, and industrial cooling compressors. The paper...... continues to describe the possible perspective in driving our technical systems to operate in a chaotic regime. An example of a technical system capable of operating under unstable conditions is the F/A-18 fighter....
How chaotic are strange nonchaotic attractors
Glendinning, Paul; Jaeger, Tobias; Keller, Gerhard
2006-01-01
We show that the classic example of quasiperiodically forced maps with strange nonchaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit sensitive dependence on initial conditions, both on the whole phase space and restricted to the attractor. The results also remain valid in more general classes of quasiperiodically forced systems. Further, we include an elementary proof of a classic result by...
Complexity and synchronization in stochastic chaotic systems
Son Dang, Thai; Palit, Sanjay Kumar; Mukherjee, Sayan; Hoang, Thang Manh; Banerjee, Santo
2016-02-01
We investigate the complexity of a hyperchaotic dynamical system perturbed by noise and various nonlinear speech and music signals. The complexity is measured by the weighted recurrence entropy of the hyperchaotic and stochastic systems. The synchronization phenomenon between two stochastic systems with complex coupling is also investigated. These criteria are tested on chaotic and perturbed systems by mean conditional recurrence and normalized synchronization error. Numerical results including surface plots, normalized synchronization errors, complexity variations etc show the effectiveness of the proposed analysis.
Frequency-Locking in Coupled Chaotic Systems
Institute of Scientific and Technical Information of China (English)
HU Bam-Bi; LIU Zong-Hua; ZHENG Zhi-Gang
2001-01-01
A novel approach is presented for measuring the phase synchronization (frequency-locking) of coupled N nonidentical oscillators, which can characterize frequency-locking for chaotic systems without well-defined phase by measuring the mean frequency. Numerical simulations confirm the existence of frequency-locking. The relations between the mean frequency and the coupling strength and the frequency mismatch are given. For the coupled hyperchaotic systems, the frequency-locking can be better characterized by more than one mean frequency curves.
Resonance eigenfunctions in chaotic scattering systems
Indian Academy of Sciences (India)
Martin Sieber
2009-09-01
We study the semiclassical structure of resonance eigenstates of open chaotic systems. We obtain semiclassical estimates for the weight of these states on different regions in phase space. These results imply that the long-lived right (left) eigenstates of the non-unitary propagator are concentrated in the semiclassical limit ħ → 0 on the backward (forward) trapped set of the classical dynamics. On this support the eigenstates display a self-similar behaviour which depends on the limiting decay rate.
Chaotic motion and collective nuclear rotation
Energy Technology Data Exchange (ETDEWEB)
Seligman, T.H.; Verbaarschot, J.J.M.; Weidenmueller, H.A.
1986-02-20
The regular and chaotic motion in the classical and quantal versions of a model Hamiltonian with two degrees of freedom are investigated. This model contains a parameter which is identified with a conserved quantum number, the total spin. In particular, transition between states differing in spin by one unit are studied. The transition is strongly collective for regular motion, and collectivity is destroyed with increasing stochasticity of the model. (orig.).
A Numeric Study on Chaotic Dislocation Emission
Institute of Scientific and Technical Information of China (English)
HonglaiTan; WeiYang
1996-01-01
Crack tip atom-string model is devised to study non-linear features of dislocation emission processes under mode II loads.Dynamic analysis shows that the atom motion at the crack tip changes from periodic to chaotic as the stress intensity factor increases.Study on the dislocation emission band reveals the phenomenon of cloud-like drifting of the dislocation core ahead of the crack tip.
Improving security of a chaotic encryption approach
Li, SJ; Mou, XQ; Cai, YL
2001-01-01
E. Alvarez et al. presented a new chaotic encryption approach recently. But soon G. Alvarez et al. broke it with four cryptanalytic methods and found some other weaknesses. In this Letter we point out why the original scheme is so vulnerable to the proposed four attacks. The chief reasons are two essential defects existing in the original scheme. Based on such a fact, we present an improved encryption scheme to obtain higher security. The cryptographic properties of the improved scheme are st...
Chaotic Identities, Love and Fathering
Directory of Open Access Journals (Sweden)
Stephen Williams
2011-08-01
Full Text Available Fathers today are confronted with constantly changing ideas on theirrole as a parent. The old traditional forms of fathering i.e. the breadwinner and protector roles are being gradually replaced by a more reflexive role that places unconditional love from their children as a central theme in a new type of reflexive parenting. This article examines the role of fatherhood through the theoreticallens of reflexive modernity. It recognises that men are increasingly becoming dependant on their children for unconditional love and this is forcing men to become more involved in the lives of their own children. The theory of reflexive modernisation is applied to a group of 40 fathers from a post-industrial area of Britain to unravel the processes and practices being used in this “new” type of parenting. This research discovers that fathers in the 21st century have numerouspressures from changing ideas about what is a good or bad father, but in the final instance it is their individualised responses to these societal and personal circumstances which create a new reflexive type of fathering. This type of fathering is therefore created by general social changes within a reflexive modern society and also by personal choice.
HF radiation emitted by chaotic leader processes
Mäkelä, J. S.; Edirisinghe, M.; Fernando, M.; Montaño, R.; Cooray, V.
2007-04-01
This paper presents direct measurements of narrowband 10 MHz HF radiation from so-called “chaotic leaders” associated with subsequent return strokes. Although the term is controversial and poorly defined, we find that more than 30% of subsequent strokes in close lightning flashes contain electric field characteristics that are best described as “chaotic”. In earlier studies, return strokes have consistently been observed to be the strongest sources of HF radiation, but the results for leader processes are less consistent. We also observe return strokes to be the main HF emitter, and the leaders before the first return stroke in a flash sequence also emit HF though somewhat less intensely. The leaders preceding subsequent strokes typically emit little or no HF radiation, whether they are dart or dart-stepped leaders. However, it was observed that the presence of a chaotic component increases the leader HF intensity dramatically Defining the HF intensity unequivocally can be problematic for processes like chaotic leaders which have a combination of continuous and impulsive phenomena. Two time-domain methods were used to measure the HF intensity, the peak energy and the RMS energy. In the frequency domain these correspond to the energy spectral density (ESD) and power spectral density (PSD), respectively. It was found that the methods are not necessarily compatible. Thus, it is suggested that to clarify future work, leader processes should be characterized by the PSD rather than the ESD.
Entanglement production in quantized chaotic systems
Indian Academy of Sciences (India)
Jayendra N Bandyopadhyay; Arul Lakshminarayan
2005-04-01
Quantum chaos is a subject whose major goal is to identify and to investigate different quantum signatures of classical chaos. Here we study entanglement production in coupled chaotic systems as a possible quantum indicator of classical chaos. We use coupled kicked tops as a model for our extensive numerical studies. We find that, in general, chaos in the system produces more entanglement. However, coupling strength between two subsystems is also a very important parameter for entanglement production. Here we show how chaos can lead to large entanglement which is universal and describable by random matrix theory (RMT). We also explain entanglement production in coupled strongly chaotic systems by deriving a formula based on RMT. This formula is valid for arbitrary coupling strengths, as well as for sufficiently long time. Here we investigate also the effect of chaos on the entanglement production for the mixed initial state. We find that many properties of the mixed-state entanglement production are qualitatively similar to the pure state entanglement production. We however still lack an analytical understanding of the mixed-state entanglement production in chaotic systems.
Experimental study of the chaotic waterwheel
Rutherford, George; Erxleben, Amy; Rosa, Epaminondas, Jr.
2007-03-01
The chaotic waterwheel is often given as an example of a mechanical system that can exhibit chaotic behavior. Its early demonstration by Malkus and the realization that it can be modeled by the Lorenz equations has secured it a prominent place in almost every general presentation of chaos. It seems quite surprising, then, that no experimental investigations of this textbook system have ever been published. To fill this historic gap, and to initiate an experimental study of this incredibly rich dynamic system, our lab has constructed a research-grade waterwheel consisting of a vacuum-formed polycarbonate frame in which 36 cylindrical cells are mounted on an 18 inch diameter. The wheel and its axis can be tilted, and water is fed into the top of the wheel and drains out through thin tubes at the bottom of each cell. An aluminum skirt at the wheel's periphery passes through a variable gap magnet to provide magnetic braking. Angular time series data are collected with an absolute rotary encoder. The data are smoothed and angular velocity and acceleration are calculated via fast fourier transforms. The data show quasi-uniform rotation as well as periodic and chaotic motion and agree fairly well with computer simulations of the idealized wheel equations. We will discuss differences between the experimental data and the simulation predictions as well as plans for future studies.
Scarring of Dirac fermions in chaotic billiards.
Ni, Xuan; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2012-07-01
Scarring in quantum systems with classical chaotic dynamics is one of the most remarkable phenomena in modern physics. Previous works were concerned mostly with nonrelativistic quantum systems described by the Schrödinger equation. The question remains outstanding of whether truly relativistic quantum particles that obey the Dirac equation can scar. A significant challenge is the lack of a general method for solving the Dirac equation in closed domains of arbitrary shape. In this paper, we develop a numerical framework for obtaining complete eigensolutions of massless fermions in general two-dimensional confining geometries. The key ingredients of our method are the proper handling of the boundary conditions and an efficient discretization scheme that casts the original equation in a matrix representation. The method is validated by (1) comparing the numerical solutions to analytic results for a geometrically simple confinement and (2) verifying that the calculated energy level-spacing statistics of integrable and chaotic geometries agree with the known results. Solutions of the Dirac equation in a number of representative chaotic geometries establish firmly the existence of scarring of Dirac fermions.
Front propagation in a chaotic flow field
Mehrvarzi, C. O.; Paul, M. R.
2014-07-01
We investigate numerically the dynamics of a propagating front in the presence of a spatiotemporally chaotic flow field. The flow field is the three-dimensional time-dependent state of spiral defect chaos generated by Rayleigh-Bénard convection in a spatially extended domain. Using large-scale parallel numerical simulations, we simultaneously solve the Boussinesq equations and a reaction-advection-diffusion equation with a Fischer-Kolmogorov-Petrovskii-Piskunov reaction for the transport of the scalar species in a large-aspect-ratio cylindrical domain for experimentally accessible conditions. We explore the front dynamics and geometry in the low-Damköhler-number regime, where the effect of the flow field is significant. Our results show that the chaotic flow field enhances the front propagation when compared with a purely cellular flow field. We quantify this enhancement by computing the spreading rate of the reaction products for a range of parameters. We use our results to quantify the complexity of the three-dimensional front geometry for a range of chaotic flow conditions.
Chaotic inflation with curvaton induced running
Sloth, Martin S
2014-01-01
The apparent tension between the the recent BICEP2 data and the Planck data might be removed by allowing for a large running in the spectral index as suggested by the BICEP2 collaboration, but in disagreement with prediction of the simplest model of chaotic inflation. The large field chaotic model is sensitive to UV physics, and the non-trivial running of the spectral index hinted by the BICEP2 data could therefore be telling us some additional new information about the UV completion of inflation. However, before we can draw such strong conclusions with confidence, we might first have to carefully exclude the alternatives. Assuming monomial chaotic inflation is the right theory of inflation, we therefore explore the possibility that the running could be due to some other less UV sensitive degree of freedom. As an example, we ask if it is possible that the curvature perturbation spectrum has a contribution from a curvaton, which makes up for the large running in the spectrum. We find that this effect could mas...
Chaotic Mixing in Three Dimensional Porous Media
Lester, Daniel R; Borgne, Tanguy Le
2016-01-01
Under steady flow conditions, the topological complexity inherent to all random 3D porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a three-dimensional (3D) fluid mechanical analogue of the baker's map which rapidly accelerates scalar mixing in the presence of molecular di?usion. Hence pore-scale fluid mixing is governed by the interplay between chaotic advection, molecular di?usion and the broad (power-law) distribution of fluid particle travel times which arise from the non-slip condition at pore walls. To understand and quantify mixing in 3D porous media, we consider these processes in a model 3D open porous network and develop a novel stretching continuous time random walk (CTRW) which provides analytic estimates of pore-scale mixing which compare well with direct numerical simulations. We ?nd that chaotic advection inherent to 3D porous media imparts scalar mixing which scales exponentially with longitudi...
Exact Eigenfunctions of a Chaotic System
Ausländer, O M
1997-01-01
The interest in the properties of quantum systems, whose classical dynamics are chaotic, derives from their abundance in nature. The spectrum of such systems can be related, in the semiclassical approximation (SCA), to the unstable classical periodic orbits, through Gutzwiller's trace formula. The class of systems studied in this work, tiling billiards on the pseudo-sphere, is special in this correspondence being exact, via Selberg's trace formula. In this work, an exact expression for Green's function (GF) and the eigenfunctions (EF) of tiling billiards on the pseudo-sphere, whose classical dynamics are chaotic, is derived. GF is shown to be equal to the quotient of two infinite sums over periodic orbits, where the denominator is the spectral determinant. Such a result is known to be true for typical chaotic systems, in the leading SCA. From the exact expression for GF, individual EF can be identified. In order to obtain a SCA by finite series for the infinite sums encountered, resummation by analytic contin...
Wave dynamics of regular and chaotic rays
Energy Technology Data Exchange (ETDEWEB)
McDonald, S.W.
1983-09-01
In order to investigate general relationships between waves and rays in chaotic systems, I study the eigenfunctions and spectrum of a simple model, the two-dimensional Helmholtz equation in a stadium boundary, for which the rays are ergodic. Statistical measurements are performed so that the apparent randomness of the stadium modes can be quantitatively contrasted with the familiar regularities observed for the modes in a circular boundary (with integrable rays). The local spatial autocorrelation of the eigenfunctions is constructed in order to indirectly test theoretical predictions for the nature of the Wigner distribution corresponding to chaotic waves. A portion of the large-eigenvalue spectrum is computed and reported in an appendix; the probability distribution of successive level spacings is analyzed and compared with theoretical predictions. The two principal conclusions are: 1) waves associated with chaotic rays may exhibit randomly situated localized regions of high intensity; 2) the Wigner function for these waves may depart significantly from being uniformly distributed over the surface of constant frequency in the ray phase space.
Transient chaotic transport in dissipative drift motion
Energy Technology Data Exchange (ETDEWEB)
Oyarzabal, R.S. [Pós-Graduação em Ciências/Física, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, PR (Brazil); Szezech, J.D. [Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, PR (Brazil); Batista, A.M., E-mail: antoniomarcosbatista@gmail.com [Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, 84030-900, Ponta Grossa, PR (Brazil); Souza, S.L.T. de [Departamento de Física e Matemática, Universidade Federal de São João del Rei, 36420-000, Ouro Branco, MG (Brazil); Caldas, I.L. [Instituto de Física, Universidade de São Paulo, 05315-970, São Paulo, SP (Brazil); Viana, R.L. [Departamento de Física, Universidade Federal do Paraná, 81531-990, Curitiba, PR (Brazil); Sanjuán, M.A.F. [Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid (Spain)
2016-04-22
Highlights: • We consider a situation for which a chaotic transient is present in the dynamics of the two-wave model with damping. • The damping in plasma models can be a way for study a realistic behavior of confinement due the collisional effect. • The escape time as a function of the damping obey a power-law scaling. • We have made a qualitative transport analysis with a simple model that can be useful for more complete models. • We have shown that the pattern of the basin of attraction depends on the damping parameter. - Abstract: We investigate chaotic particle transport in magnetised plasmas with two electrostatic drift waves. Considering dissipation in the drift motion, we verify that the removed KAM surfaces originate periodic attractors with their corresponding basins of attraction. We show that the properties of the basins depend on the dissipation and the space-averaged escape time decays exponentially when the dissipation increases. We find positive finite time Lyapunov exponents in dissipative drift motion, consequently the trajectories exhibit transient chaotic transport. These features indicate how the transient plasma transport depends on the dissipation.
Coexistence of exponentially many chaotic spin-glass attractors.
Peleg, Y; Zigzag, M; Kinzel, W; Kanter, I
2011-12-01
A chaotic network of size N with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated. For a load α = P/N chaotic network functions as an associative memory of 2P attractors with macroscopic basin of attractions which decrease with α. At finite α, a chaotic spin-glass phase exists, where the number of distinct chaotic attractors scales exponentially with N. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the N chaotic units or freezing with respect to the P patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations.
Cipher quasi-chaotic code for frequency hopping communications
Institute of Scientific and Technical Information of China (English)
王宏霞; 何晨; 虞厥邦
2004-01-01
The chaotic frequency hopping (FH) communication systems have been presented so far. The chaotic sequences possesses good randomness and sensitive dependence on initial conditions, which is quite advantageous to run the FH codes in code-division multiple access (CDMA) systems. But the finite precision of computation and the fact of the low-dimensional chaos predicted easily cause difficulty in chaotic application. In this paper, some disadvantages associated with the conventional FH codes and the chaotic code scrambled by m-sequences are reviewed briefly. In order to overcome these drawbacks to some extents, a new higher performance FH code called cipher quasi-chaotic (CQC) code is proposed,which is generated by combining the clock-controlled stream cipher technique and chaotic dynamics. Performance analysis applying in FH communication systems of this kind of code is given. The privacy of the CQC sequence is also analyzed.
Energy Technology Data Exchange (ETDEWEB)
Barnes, Rory; Deitrick, Russell; Quinn, Thomas R. [Astronomy Department, University of Washington, Box 951580, Seattle, WA 98195 (United States); Greenberg, Richard [Lunar and Planetary Laboratory, University of Arizona, 1629 E. University Boulevard, Tucson, AZ 86716 (United States); Raymond, Sean N., E-mail: rory@astro.washington.edu [NASA Astrobiology Institute-Virtual Planetary Laboratory Lead Team (United States)
2015-03-10
We present N-body simulations of resonant planets with inclined orbits that show chaotically evolving eccentricities and inclinations that can persist for at least 10 Gyr. A wide range of behavior is possible, from fast, low amplitude variations to systems in which eccentricities reach 0.9999 and inclinations 179.°9. While the orbital elements evolve chaotically, at least one resonant argument always librates. We show that the HD 73526, HD 45364, and HD 60532 systems may be in chaotically evolving resonances. Chaotic evolution is apparent in the 2:1, 3:1, and 3:2 resonances, and for planetary masses from lunar- to Jupiter-mass. In some cases, orbital disruption occurs after several gigayears, implying the mechanism is not rigorously stable, just long-lived relative to the main sequence lifetimes of solar-type stars. Planet-planet scattering appears to yield planets in inclined resonances that evolve chaotically in about 0.5% of cases. These results suggest that (1) approximate methods for identifying unstable orbital architectures may have limited applicability, (2) the observed close-in exoplanets may be produced during epochs of high eccentricit induced by inclined resonances, (3) those exoplanets' orbital planes may be misaligned with the host star's spin axis, (4) systems with resonances may be systematically younger than those without, (5) the distribution of period ratios of adjacent planets detected via transit may be skewed due to inclined resonances, and (6) potentially habitable planets may have dramatically different climatic evolution than Earth. The Gaia spacecraft is capable of discovering giant planets in these types of orbits.
The chaotic set and the cross section for chaotic scattering beyond two degrees of freedom
Jung, C; Seligman, T H; Zapfe, W P K
2010-01-01
This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step toward a more general understanding of chaotic scattering in higher dimensions. Despite of the strong restrictions it breaks the essential simplicity implicit in any two-dimensional time-independent scattering problem. Introducing the third degree of freedom by breaking a continuous symmetry, we first explore the topological structure of the homoclinic/heteroclinic tangle and the structures in the scattering functions. Then we work out implications of these structures for the doubly differential cross section. The most prominent structures in the cross section are rainbow singularities. They form a fractal pattern which reflects the fractal structure of the chaotic invariant set. This allows to determine structures in the cross section from the invariant set and conversely, to obtain information about the topology of the invariant set from the cross section. The latter ...
Directory of Open Access Journals (Sweden)
Alireza Khosravi
2012-03-01
Full Text Available This paper deals with the design of optimal backstepping controller, by using the chaotic particle swarm optimization (CPSO algorithm to control of chaos in Lure like chaotic system. The backstepping method consists of parameters which could have positive values. The parameters are usually chosen optional by trial and error method. The controlled system provides different behaviors for different values of the parameters. It is necessary to select proper parameters to obtain a good response, because the improper selection of the parameters leads to inappropriate responses or even may lead to instability of the system. The proposed optimal backstepping controller without trial and error determines the parameters of backstepping controller automatically and intelligently by minimizing the Integral of Time multiplied Absolute Error (ITAE and squared controller output. Finally, the efficiency of the proposed optimal backstepping controller (OBSC is illustrated by implementing the method on the Lure like chaotic system.
Higher-dimensional chaotic dynamics of a composite laminated piezoelectric rectangular plate
Institute of Scientific and Technical Information of China (English)
ZHANG Wei; GAO MeiJuan; YAO MingHui; YAO ZhiGang
2009-01-01
The analysis on the chaotic dynamics of a six-dimensional nonlinear system which represents the averaged equation of a composite laminated piezoelectric rectangular plate is given for the first time. The theory of normal form and the energy-phase method are combined to investigate the higher-dimensional chaotic dynamics of the composite laminated piezoelectric rectangular plate. Firstly, the theory of normal form is used to reduce the six-dimensional averaged equation to the simpler normal form.Then, the energy-phase method is extended to analyze the global bifurcations and chaotic dynamics of a six-dimensional nonlinear system. The analysis results indicate that there exist the homoclinic bifurcation and Shilnikov type multi-pulse chaos for the composite laminated piezoelectric rectangular plate. Finally, numerical simulations are also used to investigate the nonlinear dynamic characteristics of the composite laminated piezoelectric rectangular plate. The results of numerical simulations also demonstrate that there exist the chaotic motions and the multi-pulse jumping orbits of the composite laminated piezoelectric rectangular plate.
Higher-dimensional chaotic dynamics of a composite laminated piezoelectric rectangular plate
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The analysis on the chaotic dynamics of a six-dimensional nonlinear system which represents the averaged equation of a composite laminated piezoelectric rectangular plate is given for the first time. The theory of normal form and the energy-phase method are combined to investigate the higher-dimen-sional chaotic dynamics of the composite laminated piezoelectric rectangular plate. Firstly,the theory of normal form is used to reduce the six-dimensional averaged equation to the simpler normal form. Then,the energy-phase method is extended to analyze the global bifurcations and chaotic dynamics of a six-dimensional nonlinear system. The analysis results indicate that there exist the homoclinic bi-furcation and Shilnikov type multi-pulse chaos for the composite laminated piezoelectric rectangular plate. Finally,numerical simulations are also used to investigate the nonlinear dynamic characteristics of the composite laminated piezoelectric rectangular plate. The results of numerical simulations also demonstrate that there exist the chaotic motions and the multi-pulse jumping orbits of the composite laminated piezoelectric rectangular plate.
A new substitution-diffusion based image cipher using chaotic standard and logistic maps
Patidar, Vinod; Pareek, N. K.; Sud, K. K.
2009-07-01
In this paper, we propose a new loss-less symmetric image cipher based on the widely used substitution-diffusion architecture which utilizes chaotic standard and logistic maps. It is specifically designed for the coloured images, which are 3D arrays of data streams. The initial condition, system parameter of the chaotic standard map and number of iterations together constitute the secret key of the algorithm. The first round of substitution/confusion is achieved with the help of intermediate XORing keys calculated from the secret key. Then two rounds of diffusion namely the horizontal and vertical diffusions are completed by mixing the properties of horizontally and vertically adjacent pixels, respectively. In the fourth round, a robust substitution/confusion is accomplished by generating an intermediate chaotic key stream (CKS) image in a novel manner with the help of chaotic standard and logistic maps. The security and performance of the proposed image encryption technique has been analyzed thoroughly using various statistical analysis, key sensitivity analysis, differential analysis, key space analysis, speed analysis, etc. Results of the various types of analysis are encouraging and suggest that the proposed image encryption technique is able to manage the trade offs between the security and speed and hence suitable for the real-time secure image and video communication applications.
Hebecker, Arthur; Witkowski, Lukas T
2014-01-01
We analyze string-theoretic large-field inflation in the regime of spontaneously-broken supergravity with conventional moduli stabilization by fluxes and non-perturbative effects. The main ingredient is a shift-symmetric Kahler potential, supplemented by flux-induced shift symmetry breaking in the superpotential. The central technical observation is that all these features are present for D7-brane position moduli in Type IIB orientifolds. On the one hand, in the large complex structure regime they inherit a shift symmetry from their mirror-dual Type IIA Wilson lines. On the other hand, the Type IIB flux superpotential generically breaks this shift symmetry and allows, by appealing to the large flux discretuum, to tune the relevant coefficients to be small. The shift-symmetric direction in D7-brane moduli space can then play the role of the inflaton: While the D7-brane circles a certain trajectory on the Calabi-Yau many times, the corresponding F-term energy density grows only very slowly, thanks to the above-...
Scaling Features of Multimode Motions in Coupled Chaotic Oscillators
DEFF Research Database (Denmark)
Pavlov, A.N.; Sosnovtseva, Olga; Mosekilde, Erik
2003-01-01
Two different methods (the WTMM- and DFA-approaches) are applied to investigate the scaling properties in the return-time sequences generated by a system of two coupled chaotic oscillators. Transitions from twomode asynchronous dynamics (torus or torus-Chaos) to different states of chaotic phase...... synchronization are found to significantly reduce the degree of multiscality. The influence of external noise on the possibility of distinguishing the various chaotic states is considered....
Control of a Unified Chaotic System via Single Variable Feedback
Guo, Rong-Wei; Vincent E., U.
2009-09-01
Based on the LaSalle invariance principle, we propose a simple adaptive-feedback for controlling the unified chaotic system. We show explicitly with numerical proofs that our method can easily achieve the control of chaos in the unified chaotic system using only a single variable feedback. The present controller, to our knowledge, is the simplest control scheme for controlling a unified chaotic system.
Modified scaling function projective synchronization of chaotic systems
Xu, Yu-Hua; Zhou, Wu-Neng; Fang, Jian-An
2011-09-01
This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point, a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle's invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.
Implementation of a new chaotic encryption system and synchronization
Institute of Scientific and Technical Information of China (English)
Long Min; Peng Fei; Qiu Shuisheng; Chen Yanfeng
2006-01-01
A new kind of secure communication system which combines the chaotic encryption means with the conventional encryption method is discussed. With the analysis results and the experiment data, the anti-attack ability of this communication system is significantly improved compared to that of the either method. At the same time, a new method of chaotic synchronization is proposed. With a small mixed discrete chaotic signal, it is quickly to synchronize the communication and a good security performance is ensured.
Circuit realization of the fractional-order unified chaotic system
Institute of Scientific and Technical Information of China (English)
Chen Xiang-Rong; Liu Chong-Xin; Wang Fa-Qiang
2008-01-01
This paper studies the chaotic behaviours of the fractional-order unified chaotic system.Based on the approximation method in frequency domain,it proposes an electronic circuit model of tree shape to realize the fractional-order operator.According to the tree shape model,an electronic circuit is designed to realize the 2.7-order unified chaotic system.Numerical simulations and circuit experiments have verified the existence of chaos in the fraction-order unified system.
Control uncertain continuous-time chaotic dynamical system
Institute of Scientific and Technical Information of China (English)
齐冬莲; 赵光宙
2003-01-01
The new chaos control method presented in this paper is useful for taking advantage of chaos. Based on sliding mode control theory, this paper provides a switching manifold controlling strategy of chaotic system, and also gives a kind of adaptive parameters estimated method to estimate the unknown systems' parameters by which chaotic dynamical system can be synchronized. Taking the Lorenz system as example, and with the help of this controlling strategy, we can synchronize chaotic systems with unknown parameters and different initial conditions.
Projective synchronization in fractional order chaotic systems and its control
Li, Chunguang
2006-01-01
The chaotic dynamics of fractional (non-integer) order systems have begun to attract much attention in recent years. In this paper, we study the projective synchronization in two coupled fractional order chaotic oscillators. It is shown that projective synchronization can also exist in coupled fractional order chaotic systems. A simple feedback control method for controlling the scaling factor onto a desired value is also presented.
Predicting Chaotic Time Series Using Recurrent Neural Network
Institute of Scientific and Technical Information of China (English)
ZHANG Jia-Shu; XIAO Xian-Ci
2000-01-01
A new proposed method, i.e. the recurrent neural network (RNN), is introduced to predict chaotic time series. The effectiveness of using RNN for making one-step and multi-step predictions is tested based on remarkable few datum points by computer-generated chaotic time series. Numerical results show that the RNN proposed here is a very powerful tool for making prediction of chaotic time series.
Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity
Jeevarekha, A.; Paul Asir, M.; Philominathan, P.
2016-06-01
This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.
Control uncertain continuous-time chaotic dynamical system.
Qi, Dong-Lian; Zhao, Guang-Zhou
2003-01-01
The new chaos control method presented in this paper is useful for taking advantage of chaos. Based on sliding mode control theory, this paper provides a switching manifold controlling strategy of chaotic system, and also gives a kind of adaptive parameters estimated method to estimate the unknown systems' parameters by which chaotic dynamical system can be synchronized. Taking the Lorenz system as example, and with the help of this controlling strategy, we can synchronize chaotic systems with unknown parameters and different initial conditions.
Universal and nonuniversal properties of wave-chaotic scattering systems.
Yeh, Jen-Hao; Hart, James A; Bradshaw, Elliott; Antonsen, Thomas M; Ott, Edward; Anlage, Steven M
2010-02-01
Prediction of the statistics of scattering in typical wave-chaotic systems requires combining system-specific information with universal aspects of chaotic scattering as described by random matrix theory. This Rapid Communication shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically calculated in terms of ray trajectories between ports. Theoretical predictions are compared with experimental results for a microwave billiard, demonstrating that the theory successfully uncovered universal statistics of wave-chaotic scattering systems.
Directory of Open Access Journals (Sweden)
Arthur Hebecker
2014-10-01
Full Text Available We analyze string-theoretic large-field inflation in the regime of spontaneously-broken supergravity with conventional moduli stabilization by fluxes and non-perturbative effects. The main ingredient is a shift-symmetric Kähler potential, supplemented by flux-induced shift symmetry breaking in the superpotential. The central technical observation is that all these features are present for D7-brane position moduli in Type IIB orientifolds, potentially allowing for a realization of the axion monodromy proposal in a string theory compactification. Furthermore, our model is explicit enough to address issues of control and moduli stabilization quantitatively. On the one hand, in the large complex structure regime the D7-brane position moduli inherit a shift symmetry from their mirror-dual Type IIA Wilson lines. On the other hand, the Type IIB flux superpotential generically breaks this shift symmetry and allows, by appealing to the large flux discretuum, to tune the relevant coefficients to be small. The shift-symmetric direction in D7-brane moduli space can then play the role of the inflaton: While the D7-brane circles a certain trajectory on the Calabi–Yau many times, the corresponding F-term energy density grows only very slowly, thanks to the above-mentioned tuning of the flux. To be successful our model requires that the dilaton, all complex structure moduli and all D7-brane moduli except the inflaton are fixed at leading order by fluxes. Then the large-field inflationary trajectory can be realized in a regime where Kähler, complex structure and other brane moduli are stabilized in a conventional manner, as we demonstrate using the example of the Large Volume Scenario.
Hebecker, Arthur; Kraus, Sebastian C.; Witkowski, Lukas T.
2014-10-01
We analyze string-theoretic large-field inflation in the regime of spontaneously-broken supergravity with conventional moduli stabilization by fluxes and non-perturbative effects. The main ingredient is a shift-symmetric Kähler potential, supplemented by flux-induced shift symmetry breaking in the superpotential. The central technical observation is that all these features are present for D7-brane position moduli in Type IIB orientifolds, potentially allowing for a realization of the axion monodromy proposal in a string theory compactification. Furthermore, our model is explicit enough to address issues of control and moduli stabilization quantitatively. On the one hand, in the large complex structure regime the D7-brane position moduli inherit a shift symmetry from their mirror-dual Type IIA Wilson lines. On the other hand, the Type IIB flux superpotential generically breaks this shift symmetry and allows, by appealing to the large flux discretuum, to tune the relevant coefficients to be small. The shift-symmetric direction in D7-brane moduli space can then play the role of the inflaton: While the D7-brane circles a certain trajectory on the Calabi-Yau many times, the corresponding F-term energy density grows only very slowly, thanks to the above-mentioned tuning of the flux. To be successful our model requires that the dilaton, all complex structure moduli and all D7-brane moduli except the inflaton are fixed at leading order by fluxes. Then the large-field inflationary trajectory can be realized in a regime where Kähler, complex structure and other brane moduli are stabilized in a conventional manner, as we demonstrate using the example of the Large Volume Scenario.
Tracking control of chaotic dynamical systems with feedback linearization
Institute of Scientific and Technical Information of China (English)
QI Dong-lian; MA Guo-jin
2005-01-01
A new method was proposed for tracking the desired output of chaotic dynamical system using the feedback linearization and nonlinear extended statement observer method. The feedback linearization was used to convert the nonlinear chaotic system into linear system. The extended Luenberger-like statements observer was designed to reconstructing and observing the unmeasured statements when the tracking controller was designed. By this way, the chaotic system could be forced to track variable desired output, which could be a time variant function or an equilibrium points.Taken the Lorenz chaotic system as example, the simulation results show the validity of the conclusion and effectiveness of the algorithm.
Projective Synchronization in Time-Delayed Chaotic Systems
Institute of Scientific and Technical Information of China (English)
FENG Cun-Fang; ZHANG Yan; WANG Ying-Hai
2006-01-01
For the first time, we report on projective synchronization between two time delay chaotic systems with single time delays. It overcomes some limitations of the previous wort, where projective synchronization has been investigated only in finite-dimensional chaotic systems, so we can achieve projective synchronization in infinite-dimensional chaotic systems. We give a general method with which we can achieve projective synchronization in time-delayed chaotic systems. The method is illustrated using the famous delay-differential equations related to optical bistability. Numerical simulations fully support the analytical approach.
Chaotic attractor transforming control of hybrid Lorenz-Chen system
Institute of Scientific and Technical Information of China (English)
Qi Dong-Lian; Wang Qiao; Gu Hong
2008-01-01
Based on passive theory, this paper studies a hybrid chaotic dynamical system from the mathematics perspective to implement the control of system stabilization.According to the Jacobian matrix of the nonlinear system, the stabilization control region is gotten.The controller is designed to stabilize fast the minimum phase Lorenz-Chen chaotic system after equivalently transforming from chaotic system to passive system. The simulation results show that the system not only can be controlled at the different equilibria, but also can be transformed between the different chaotic attractors.
Adaptive generalized functional synchronization of Chaotic systems with unknown parameters
Institute of Scientific and Technical Information of China (English)
Wang Dong-Feng; Han Pu
2008-01-01
A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed,based on a unified mathematical expression of a large class of chaotic system.Self-adaptive parameter law and control law are given in the form of a theorem.The synchronization between the three-dimensional R(o)ssler chaotic system and the four-dimensional Chen's hyper-chaotic system is studied as an example for illustration.The computer simulation results demonstrate the feasibility of the method proposed.
Infinite-Dimensional Linear Dynamical Systems with Chaoticity
Fu Xin Chu; Fu, Xin-Chu; Duan, Jinqiao
1998-01-01
The authors present two results on infinite-dimensional linear dynamical systems with chaoticity. One is about the chaoticity of the backward shift map in the space of infinite sequences on a general Fréchet space. The other is about the chaoticity of a translation map in the space of real continuous functions. The chaos is shown in the senses of both Li-Yorke and Wiggins. Treating dimensions as freedoms, the two results imply that in the case of an infinite number of freedoms, a system may exhibit complexity even when the action is linear. Finally, the authors discuss physical applications of infinite-dimensional linear chaotic dynamical systems.
Adaptive Synchronization of Memristor-based Chaotic Neural Systems
Directory of Open Access Journals (Sweden)
Xiaofang Hu
2014-11-01
Full Text Available Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adaptive backstepping approach. A systematic design procedure is presented. Simulation results have demonstrated the effectiveness of the proposed adaptive synchronization method and its potential in practical application of memristive chaotic oscillators in secure communication.
On periodic and chaotic regions in the Mandelbrot set
Energy Technology Data Exchange (ETDEWEB)
Pastor, G. [Instituto de Fisica Aplicada, Consejo Superior de Investigaciones Cientificas, Serrano 144, 28006 Madrid (Spain)]. E-mail: gerardo@iec.csic.es; Romera, M. [Instituto de Fisica Aplicada, Consejo Superior de Investigaciones Cientificas, Serrano 144, 28006 Madrid (Spain); Alvarez, G. [Instituto de Fisica Aplicada, Consejo Superior de Investigaciones Cientificas, Serrano 144, 28006 Madrid (Spain); Arroyo, D. [Instituto de Fisica Aplicada, Consejo Superior de Investigaciones Cientificas, Serrano 144, 28006 Madrid (Spain); Montoya, F. [Instituto de Fisica Aplicada, Consejo Superior de Investigaciones Cientificas, Serrano 144, 28006 Madrid (Spain)
2007-04-15
We show here in a graphic and simple way the relation between the periodic and chaotic regions in the Mandelbrot set. Since the relation between the periodic and chaotic regions in a one-dimensional (1D) quadratic set is already well known, we shall base on it to extend the results to the Mandelbrot set. We shall see that in the same way as the hyperbolic components of the period-doubling cascade determines the chaotic bands structure in 1D quadratic sets, the periodic region determines the chaotic region in the Mandelbrot set.
Chaotic Dynamics of Falling Disks: from Maxwell to Bar Tricks.
Field, Stuart
1998-03-01
Understanding the motion of flat objects falling in a viscous medium dates back to at least Newton and Maxwell, and is relevant to problems in meteorology, sedimentology, aerospace and chemical engineering, and nori/disks/pub.html>bar wagering strategies. Recent theoretical studies have emphasized the role played by deterministic chaos. Here we nori/falling.html>report(S. B. Field, M. Klaus, M. G. Moore, and F. Nori, Nature 388), 252 (1997) experimental observations and theoretical analysis of the dynamics of disks falling in water/glycerol mixtures. We find four distinct types of motion, and map out a ``phase diagram'' in the appropriate variables. The apparently complex behavior of the disks can be reduced to a series of one-dimensional maps which display a discontinuity at the crossover from periodic and chaotic motion. This discontinuity leads to an unusual intermittency transition between the two behaviors, which has not previously been observed experimentally in any system.
Extending the scope of holographic mutual information and chaotic behavior
Sircar, Nilanjan; Tangarife, Walter
2016-01-01
We extend the use of holography to investigate the scrambling properties of various physical systems. Specifically, we consider: (i) non-conformal backgrounds of black $Dp$ branes, (ii) asymptotically Lifshitz black holes, and (iii) black $AdS$ solutions of Gauss-Bonnet gravity. We use the disruption of the entanglement entropy as a probe of the chaotic features of such systems. Our analysis shows that these theories share the same type of behavior as conformal theories as they undergo chaos; however, in the case of Gauss-Bonnet gravity, we find a stark difference in the evolution of the mutual information for negative Gauss-Bonnet coupling. This may signal an inconsistency of the latter.
Chaotic or just complicated? Ball bouncing down the stairs
Gruiz, Márton; Meszéna, Tamás; Tél, Tamás
2017-09-01
The aim of this study is to investigate the bouncing dynamics of a small elastic ball on a rectangular stairway and to determine if its dynamics is chaotic. We derive a simple nonlinear recursion for the coordinates of the collisions from which the type of dynamics cannot be predicted. Numerical simulations indicate that stationary bouncing always sets in asymptotically, and is typically quasi-periodic. The dependence on the coefficient of restitution can be very complicated, yet the dynamics is found to be nonchaotic. Only elementary mathematics is required for the calculations, and we offer a piece of user-friendly demo software on our website, http://crnl.hu/stairway, to facilitate further understanding of this complex phenomenon.
Extending the scope of holographic mutual information and chaotic behavior
Sircar, Nilanjan; Sonnenschein, Jacob; Tangarife, Walter
2016-05-01
We extend the use of holography to investigate the scrambling properties of various physical systems. Specifically, we consider: (i) non-conformal backgrounds of black Dp branes, (ii) asymptotically Lifshitz black holes, and (iii) black AdS solutions of Gauss-Bonnet gravity. We use the disruption of the entanglement entropy as a probe of the chaotic features of such systems. Our analysis shows that these theories share the same type of behavior as conformal theories as they undergo chaos; however, in the case of Gauss-Bonnet gravity, we find a stark difference in the evolution of the mutual information for negative Gauss-Bonnet coupling. This may signal an inconsistency of the latter.
Underwater Chaotic Lidar using Blue Laser Diodes
Rumbaugh, Luke K.
The thesis proposes and explores an underwater lidar system architecture based on chaotic modulation of recently introduced, commercially available, low cost blue laser diodes. This approach is experimentally shown to allow accurate underwater impulse response measurements while eliminating the need for several major components typically found in high-performance underwater lidar systems. The proposed approach is to: 1. Generate wideband, noise-like intensity modulation signals using optical chaotic modulation of blue-green laser diodes, and then 2. Use this signal source to develop an underwater chaotic lidar system that uses no electrical signal generator, no electro-optic modulator, no optical frequency doubler, and no large-aperture photodetector. The outcome of this thesis is the demonstration of a new underwater lidar system architecture that could allow high resolution ranging, imaging, and water profiling measurements in turbid water, at a reduced size, weight, power and cost relative to state-of-the-art high-performance underwater lidar sensors. This work also makes contributions to the state of the art in optics, nonlinear dynamics, and underwater sensing by demonstrating for the first time: 1. Wideband noise-like intensity modulation of a blue laser diode using no electrical signal generator or electro-optic modulator. Optical chaotic modulation of a 462 nm blue InGaN laser diode by self-feedback is explored for the first time. The usefulness of the signal to chaotic lidar is evaluated in terms of bandwidth, modulation depth, and autocorrelation peak-to-sidelobe-ratio (PSLR) using both computer and laboratory experiments. In laboratory experiments, the optical feedback technique is shown to be effective in generating wideband, noise-like chaotic signals with strong modulation depth when the diode is operated in an external-cavity dominated state. The modulation signal strength is shown to be limited by the onset of lasing within the diode's internal
Rosselló, Josep L; Canals, Vicens; Oliver, Antoni; Morro, Antoni
2014-08-01
The brain is characterized by performing many diverse processing tasks ranging from elaborate processes such as pattern recognition, memory or decision making to more simple functionalities such as linear filtering in image processing. Understanding the mechanisms by which the brain is able to produce such a different range of cortical operations remains a fundamental problem in neuroscience. Here we show a study about which processes are related to chaotic and synchronized states based on the study of in-silico implementation of Stochastic Spiking Neural Networks (SSNN). The measurements obtained reveal that chaotic neural ensembles are excellent transmission and convolution systems since mutual information between signals is minimized. At the same time, synchronized cells (that can be understood as ordered states of the brain) can be associated to more complex nonlinear computations. In this sense, we experimentally show that complex and quick pattern recognition processes arise when both synchronized and chaotic states are mixed. These measurements are in accordance with in vivo observations related to the role of neural synchrony in pattern recognition and to the speed of the real biological process. We also suggest that the high-level adaptive mechanisms of the brain that are the Hebbian and non-Hebbian learning rules can be understood as processes devoted to generate the appropriate clustering of both synchronized and chaotic ensembles. The measurements obtained from the hardware implementation of different types of neural systems suggest that the brain processing can be governed by the superposition of these two complementary states with complementary functionalities (nonlinear processing for synchronized states and information convolution and parallelization for chaotic).
Lorenz, HW; Nusse, HE
Goodwin's nonlinear accelerator model with periodic investment outlays is reconsidered and used as an economic example of the emergence of complex motion in nonlinear dynamical systems. In addition to chaotic attractors, the model can possess coexisting attracting periodic orbits or simple
Chaotic synchronization for a class of fractional-order chaotic systems
Institute of Scientific and Technical Information of China (English)
Zhou Ping
2007-01-01
In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-order systems, is simple and theoretically rigorous.
The chaotic set and the cross section for chaotic scattering in three degrees of freedom
Jung, C.; Merlo, O.; Seligman, T. H.; Zapfe, W. P. K.
2010-10-01
This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step towards a more general understanding of chaotic scattering in higher dimensions. Despite the strong restrictions, it breaks the essential simplicity implicit in any two-dimensional time-independent scattering problem. Introducing the third degree of freedom by breaking a continuous symmetry, we first explore the topological structure of the homoclinic/heteroclinic tangle and the structures in the scattering functions. Then we work out the implications of these structures for the doubly differential cross section. The most prominent structures in the cross section are rainbow singularities. They form a fractal pattern that reflects the fractal structure of the chaotic invariant set. This allows us to determine structures in the cross section from the invariant set and, conversely, to obtain information about the topology of the invariant set from the cross section. The latter is a contribution to the inverse scattering problem for chaotic systems.
The chaotic set and the cross section for chaotic scattering in three degrees of freedom
Energy Technology Data Exchange (ETDEWEB)
Jung, C; Seligman, T H; Zapfe, W P K [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico, Avenida Universidad s/n, Apartado Postal 48-3 Cuernavaca, Morelos (Mexico); Merlo, O, E-mail: karelz@fis.unam.m [Zurich University of Applied Sciences, Institute of Applied Simulation, Grueental, P O Box, CH-8820 Waedenswil (Switzerland)
2010-10-15
This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step towards a more general understanding of chaotic scattering in higher dimensions. Despite the strong restrictions, it breaks the essential simplicity implicit in any two-dimensional time-independent scattering problem. Introducing the third degree of freedom by breaking a continuous symmetry, we first explore the topological structure of the homoclinic/heteroclinic tangle and the structures in the scattering functions. Then we work out the implications of these structures for the doubly differential cross section. The most prominent structures in the cross section are rainbow singularities. They form a fractal pattern that reflects the fractal structure of the chaotic invariant set. This allows us to determine structures in the cross section from the invariant set and, conversely, to obtain information about the topology of the invariant set from the cross section. The latter is a contribution to the inverse scattering problem for chaotic systems.
Institute of Scientific and Technical Information of China (English)
张解放; 郑春龙; 孟剑平; 方建平
2003-01-01
With the help of variable separation approach, a quite general excitation of a new (2+l)-dimensional long dispersive wave system is derived. The chaotic behaviour, such as chaotic line soliton patterns, chaotic dromion patterns, chaotic-period patterns, and chaotic-chaotic patterns, in some new localized excitations are found by selecting appropriate functions.
Classification of ECG Using Chaotic Models
Directory of Open Access Journals (Sweden)
Khandakar Mohammad Ishtiak
2012-09-01
Full Text Available Chaotic analysis has been shown to be useful in a variety of medical applications, particularly in cardiology. Chaotic parameters have shown potential in the identification of diseases, especially in the analysis of biomedical signals like electrocardiogram (ECG. In this work, underlying chaos in ECG signals has been analyzed using various non-linear techniques. First, the ECG signal is processed through a series of steps to extract the QRS complex. From this extracted feature, bit-to-bit interval (BBI and instantaneous heart rate (IHR have been calculated. Then some nonlinear parameters like standard deviation, and coefficient of variation and nonlinear techniques like central tendency measure (CTM, and phase space portrait have been determined from both the BBI and IHR. Standard database of MIT-BIH is used as the reference data where each ECG record contains 650000 samples. CTM is calculated for both BBI and IHR for each ECG record of the database. A much higher value of CTM for IHR is observed for eleven patients with normal beats with a mean of 0.7737 and SD of 0.0946. On the contrary, the CTM for IHR of eleven patients with abnormal rhythm shows low value with a mean of 0.0833 and SD 0.0748. CTM for BBI of the same eleven normal rhythm records also shows high values with a mean of 0.6172 and SD 0.1472. CTM for BBI of eleven abnormal rhythm records show low values with a mean of 0.0478 and SD 0.0308. Phase space portrait also demonstrates visible attractor with little dispersion for a healthy person’s ECG and a widely dispersed plot in 2-D plane for the ailing person’s ECG. These results indicate that ECG can be classified based on this chaotic modeling which works on the nonlinear dynamics of the system.
Chaotic Information Processing by Extremal Black Holes
Axenides, Minos; Nicolis, Stam
2015-01-01
We review an explicit regularization of the AdS$_2$/CFT$_1$ correspondence, that preserves all isometries of bulk and boundary degrees of freedom. This scheme is useful to characterize the space of the unitary evolution operators that describe the dynamics of the microstates of extremal black holes in four spacetime dimensions. Using techniques from algebraic number theory to evaluate the transition amplitudes, we remark that the regularization scheme expresses the fast quantum computation capability of black holes as well as its chaotic nature.
Recursive backstepping control of chaotic Duffing oscillators
Energy Technology Data Exchange (ETDEWEB)
Harb, Ahmad M. [Jordan University of Science and Technology, EE Department, P.O. Box 3030, Irbid (Jordan)]. E-mail: aharb@just.edu.jo; Zaher, Ashraf A. [Oakland University, School of Engineering and Computer Science, ESE Department, DHE 137, Rochester, MI 48309 (United States); Al-Qaisia, Ahmad A. [University of Jordan, ME Department, Amman (Jordan); Zohdy, Mohammad A. [Oakland University, School of Engineering and Computer Science, ESE Department, DHE 137, Rochester, MI 48309 (United States)
2007-10-15
In this paper, the dynamics of a forced Duffing oscillator is studied by means of modern nonlinear, bifurcation and chaos theories and shows that the system is ultimately experiencing chaos. The main objective is to characterize and control chaotic behavior. A nonlinear recursive backstepping controller is proposed and the transient performance is investigated. Systematic following of a reference model is introduced. Robustness problems as well as ways to tune the controller parameters are examined. Simulation results are submitted for the uncontrolled and controlled cases, verifying the effectiveness of the proposed controller. Finally a discussion and conclusions are given with possible future extensions.
Correlations in Electrically Coupled Chaotic Lasers
Rosero, E J; Avila, J F Martinez; Khoury, A Z; Leite, J R Rios
2016-01-01
We show how two electrically coupled semiconductor lasers having optical feedback can present simultaneous anti-phase correlated fast power fluctuations, and strong in-phase synchronized spikes of chaotic power drops. This quite counter intuitive phenomenon is demonstrated experimentally and confirmed by numerical solutions of a deterministic dynamical system of rate equations. The occurrence of negative and positive cross correlation between parts of a complex system according to time scales, as proved in our simple arrangement, is relevant for the understanding and characterization of collective properties in complex networks.
Chaotic Friedmann-Robertson-Walker Cosmology
Calzetta, E A
1993-01-01
We show that the dynamics of a spatially closed Friedmann - Robertson - Walker Universe conformally coupled to a real, free, massive scalar field, is chaotic, for large enough field amplitudes. We do so by proving that this system is integrable under the adiabatic approximation, but that the corresponding KAM tori break up when non adiabatic terms are considered. This finding is confirmed by numerical evaluation of the Lyapunov exponents associated with the system, among other criteria. Chaos sets strong limitations to our ability to predict the value of the field at the Big Crunch, from its given value at the Big Bang. (Figures available on request)
Chaotic musical murmur in aortic regurgitation.
Miyahara, K; Amitani, S; Sohara, H; Kurose, M; Iwamura, H; Toyohira, H; Taira, A
1996-12-01
We report an interesting case of aortic regurgitation. Phonocardiographically, the shape of the diastolic musical murmur in this case changed in each cardiac cycle despite being in sinus rhythm, in the same posture and in the same breathing phase. Experimentally, we were able to obtain a similar noise pattern using an artificial respirator and a hemispherical silicone membrane. We concluded that the irregular and chaotic change in the shape of the diastolic musical murmur in the present case occurred due to irregular swaying of the non-coronary cusp under the influence of the Venturi effect owing to a regurgitant jet stream.
Noise-Induced Riddling in Chaotic Systems
Energy Technology Data Exchange (ETDEWEB)
Lai, Y.; Grebogi, C. [Departments of Physics and Astronomy and of Mathematics, The University of Kansas, Lawrence, Kansas 66045 (United States)]|[Institute for Plasma Research, The University of Maryland, College Park, Maryland 20742 (United States)
1996-12-01
Recent works have considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is {ital transversely} {ital stable}, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. We show that riddling can be induced by arbitrarily small random noise {ital even} {ital if} {ital the} {ital attractor} {ital is} {ital transversely} {ital unstable}, and we obtain universal scaling laws for noise-induced riddling. Our results imply that the phenomenon of riddling can be more prevalent than expected before, as noise is practically inevitable in dynamical systems. {copyright} {ital 1996 The American Physical Society.}
ADAPTIVE CONTROL AND IDENTIFICATION OF CHAOTIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
LI ZHI; HAN CHONG-ZHAO
2001-01-01
A novel adaptive control and identification on-line method is proposed for a class of chaotic system with uncertain parameters. We prove that, using the presented method, a controller and identifier is developed which can remove chaos in nonlinear systems and make the system asymptotically stabilizing to an arbitrarily desired smooth orbit. And at the same time, estimates to uncertain parameters converge to their true values. The advantage of our method over the existing result is that the controller and identifier is directly constructed by analytic formula without knowing unknown bounds about uncertain parameters in advance. A computer simulation example is given to validate the proposed approach.
Interaction of Regular and Chaotic States
De Pace, A; Weidenmüller, H A
2006-01-01
Modelling the chaotic states in terms of the Gaussian Orthogonal Ensemble of random matrices (GOE), we investigate the interaction of the GOE with regular bound states. The eigenvalues of the latter may or may not be embedded in the GOE spectrum. We derive a generalized form of the Pastur equation for the average Green's function. We use that equation to study the average and the variance of the shift of the regular states, their spreading width, and the deformation of the GOE spectrum non-perturbatively. We compare our results with various perturbative approaches.
Quantum ratchets in dissipative chaotic systems.
Carlo, Gabriel G; Benenti, Giuliano; Casati, Giulio; Shepelyansky, Dima L
2005-04-29
Using the method of quantum trajectories, we study a quantum chaotic dissipative ratchet appearing for particles in a pulsed asymmetric potential in the presence of a dissipative environment. The system is characterized by directed transport emerging from a quantum strange attractor. This model exhibits, in the limit of small effective Planck constant, a transition from quantum to classical behavior, in agreement with the correspondence principle. We also discuss parameter values suitable for the implementation of the quantum ratchet effect with cold atoms in optical lattices.
Chaotic satellite attitude control by adaptive approach
Wei, Wei; Wang, Jing; Zuo, Min; Liu, Zaiwen; Du, Junping
2014-06-01
In this article, chaos control of satellite attitude motion is considered. Adaptive control based on dynamic compensation is utilised to suppress the chaotic behaviour. Control approaches with three control inputs and with only one control input are proposed. Since the adaptive control employed is based on dynamic compensation, faithful model of the system is of no necessity. Sinusoidal disturbance and parameter uncertainties are considered to evaluate the robustness of the closed-loop system. Both of the approaches are confirmed by theoretical and numerical results.
Iorsh, Ivan; Alodjants, Alexander; Shelykh, Ivan A
2016-05-30
We studied optical response of microcavity non-equilibrium exciton-polariton Bose-Einstein condensate with saturable nonlinearity under simultaneous resonant and non-resonant pumping. We demonstrated the emergence of multistabile behavior due to the saturation of the excitonic absorption. Stable periodic Rabi-type oscillations of the excitonic and photonic condensate components in the regime of the stationary pump and their transition to the chaotic dynamics through the cascade of Hopf bifurcations by tuning of the electrical pump are revealed.
Iorsh, Ivan; Shelykh, Ivan
2016-01-01
We studied optical response of microcavity non-equilibrium exciton-polariton Bose-Einstein condensate with saturable nonlinearity under simultaneous resonant and non-resonant pumping. We demonstrated the emergence of multistabile behavior due to the satutration of the excitonic absorbtion. Stable periodic Rabi- type oscillations of the excitonic and photonic condensate components in the regime of the stationary pump and their transition to the chaotic dynamics through the cascade of Hopf bifurcations by tuning of the electrical pump are revealed.
Indian Academy of Sciences (India)
Fei Yu; Chunhua Wang; Qiuzhen Wan; Yan Hu
2013-02-01
A five-term three-dimensional (3D) autonomous chaotic system with an exponential nonlinear term is reported in this paper. Basic dynamical behaviours of the chaotic system are further investigated. Then a new synchronization phenomenon, complete switched modified function projective synchronization (CSMFPS), for this novel five-term chaotic system with uncertain parameters and disturbances is investigated. This paper extends previous work, where CSMFPS of chaotic systems means that all the state variables of the drive system synchronize with different state variables of the response system. As the synchronization scheme has many combined forms, it is a promising type of synchronization and can provide greater security in secure communication. Based on Lyapunov stability theory, a robust adaptive controller is contrived to acquire CSMFPS, parameter identification and suppress disturbances simultaneously. Finally, the Lorenz system and the new five-term chaotic system are taken as examples and the corresponding numerical simulations are presented to verify the effectiveness and feasibility of the proposed control scheme.
Impulsive Control for Fractional-Order Chaotic Systems
Institute of Scientific and Technical Information of China (English)
ZHONG Qi-Shui; BAO Jing-Fu; YU Yong-Bin; LIAO Xiao-Feng
2008-01-01
@@ We propose an impulsive control scheme for fractional-order chaotic systems. Based on the Takagi-Sugeno (T-S) fuzzy model and linear matrix inequalities (LMIs), some sufficient conditions are given to stabilize the fractional-order chaotic system via impulsive control. Numerical simulation shows the effectiveness of this approach.
A novel chaotic encryption scheme based on arithmetic coding
Energy Technology Data Exchange (ETDEWEB)
Mi Bo [Department of Computer Science and Engineering, Chongqing University, Chongqing 400044 (China)], E-mail: mi_bo@163.com; Liao Xiaofeng; Chen Yong [Department of Computer Science and Engineering, Chongqing University, Chongqing 400044 (China)
2008-12-15
In this paper, under the combination of arithmetic coding and logistic map, a novel chaotic encryption scheme is presented. The plaintexts are encrypted and compressed by using an arithmetic coder whose mapping intervals are changed irregularly according to a keystream derived from chaotic map and plaintext. Performance and security of the scheme are also studied experimentally and theoretically in detail.
Analysis of Chaotic Resonance in Izhikevich Neuron Model.
Nobukawa, Sou; Nishimura, Haruhiko; Yamanishi, Teruya; Liu, Jian-Qin
2015-01-01
In stochastic resonance (SR), the presence of noise helps a nonlinear system amplify a weak (sub-threshold) signal. Chaotic resonance (CR) is a phenomenon similar to SR but without stochastic noise, which has been observed in neural systems. However, no study to date has investigated and compared the characteristics and performance of the signal responses of a spiking neural system in some chaotic states in CR. In this paper, we focus on the Izhikevich neuron model, which can reproduce major spike patterns that have been experimentally observed. We examine and classify the chaotic characteristics of this model by using Lyapunov exponents with a saltation matrix and Poincaré section methods in order to address the measurement challenge posed by the state-dependent jump in the resetting process. We found the existence of two distinctive states, a chaotic state involving primarily turbulent movement and an intermittent chaotic state. In order to assess the signal responses of CR in these classified states, we introduced an extended Izhikevich neuron model by considering weak periodic signals, and defined the cycle histogram of neuron spikes as well as the corresponding mutual correlation and information. Through computer simulations, we confirmed that both chaotic states in CR can sensitively respond to weak signals. Moreover, we found that the intermittent chaotic state exhibited a prompter response than the chaotic state with primarily turbulent movement.
Chaotic scattering of two identical point vortex pairs revisited
DEFF Research Database (Denmark)
Tophøj, Laust Emil Hjerrild; Aref, Hassan
2008-01-01
A new numerical exploration suggests that the motion of two vortex pairs, with constituent vortices all of the same absolute circulation, displays chaotic scattering regimes. The mechanisms leading to chaotic scattering are different from the “slingshot effect” identified by Price [Phys. Fluids A 5...
Nuclear mass dependence of chaotic dynamics in Ginocchio model
Yoshinaga, N; Shigehara, T; Yoshinaga, Naotaka; Yoshida, Nobuaki; Shigehara, Takaomi
1995-01-01
The chaotic dynamics in nuclear collective motion is studied in the framework of a schematic shell model which has only monopole and quadrupole degrees of freedom. The model is shown to reproduce the experimentally observed global trend toward less chaotic motion in heavier nuclei. The relation between current approach and the earlier studies with bosonic models is discussed.
Chaotic Motion Of A Two-Link Planar Mechanism
Lokshin, Anatoly; Zak, Michail A.
1989-01-01
Report discusses global instability in orbital motion of two-link planar mechanism. Principal objective, contributes to understanding of chaotic motions in robot manipulators and other deterministic mechanical systems. Discussion begins with brief review of previous studies of chaotic motion and introduces notion of orbital instability in nonlinear systems. Introduces geometric approach useful in representation of orbital instability.
The Smallest Transistor-Based Nonautonomous Chaotic Circuit
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, Arunas
2005-01-01
A nonautonomous chaotic circuit based on one transistor, two capacitors, and two resistors is described. The mechanism behind the chaotic performance is based on “disturbance of integration.” The forward part and the reverse part of the bipolar transistor are “fighting” about the charging...
Enhancing the security of chaotic signals in binary message transmission
Kostenko, Pavlo Yu.; Symonenko, S. N.; S.G. Semenov; Vasiuta, K. S.
2009-01-01
A technique for inserting a binary message into chaotic carrier has been proposed that enhances the security of data transmission systems at the expense of destructing the behavior typical for chaotic processes on the phase plane. An algorithm for recovery of the transmitted message was obtained and its quality for different signal-to-noise levels was estimated.
Towards generalized synchronization of strictly different chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Femat, R. [Matematicas Aplicadas y Sistemas Computacionales, IPICYT, Apdo. Postal 3-90, 78291 Tangamanga, San Luis Potosi S.L.P. (Mexico)]. E-mail: rfemat@ipicyt.edu.mx; Kocarev, L. [Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0402 (United States)]. E-mail: lkocarev@ucsd.edu; Gerven, L. van [Department of Mechanical Engineering, Technische Universiteit Eindhoven (Netherlands); Monsivais-Perez, M.E. [Matematicas Aplicadas y Sistemas Computacionales, IPICYT, Camino a la Presa San Jose 2055, 78216 Lomas 4a Sec., San Luis Potosi S.L.P. (Mexico)
2005-07-11
This contribution addresses the problem of the generalized synchronization (GS) in different chaotic systems, and departs from chaotic systems in a triangular from, which can be derived from Lie derivatives. A state-feedback (full knowledge of both master and slave systems) scheme is designed, which achieves GS. The work includes illustrative examples; moreover an experimental setup is used to corroborate the obtained results.
Quantum Chaotic Environments, The Butterfly Effect, And Decoherence
Karkuszewski, Z P; Zurek, W H; Karkuszewski, Zbyszek P.; Jarzynski, Christopher; Zurek, Wojciech H.
2002-01-01
We investigate the sensitivity of quantum systems that are chaotic in a classical limit, to small perturbations of their equations of motion. This sensitivity, originally studied in the context of defining quantum chaos, is relevant to decoherence in situations when the environment has a chaotic classical counterpart.
Persistent excitation in adaptive parameter identification of uncertain chaotic system
Institute of Scientific and Technical Information of China (English)
Zhao Jun-chan; Zhang Qun-Jiao; Lu Jun-An
2011-01-01
This paper studies the parameter identification problem of chaotic systems. Adaptive identification laws are proposed to estimate the parameters of uncertain chaotic systems. It proves that the asymptotical identification is ensured by a persistently exciting condition. Additionally, the method can be applied to identify the uncertain parameters with any number. Numerical simulations are given to validate the theoretical analysis.
Homoclinic Bifurcation as a Mechanism of Chaotic Phase Synchronization
DEFF Research Database (Denmark)
Postnov, D.E.; Balanov, A.G.; Janson, N.B.;
1999-01-01
This paper demonstrates a mechanism of chaotic phase synchronization in which the transition from asynchronous to synchronous chaos is associated with the collision of the asynchronous chaotic attractor with an unstable periodic orbit. This gives rise to a hysteretic transition with the two chaot...
Secure Image Encryption Based On a Chua Chaotic Noise Generator
Directory of Open Access Journals (Sweden)
A. S. Andreatos
2013-10-01
Full Text Available This paper presents a secure image cryptography telecom system based on a Chua's circuit chaotic noise generator. A chaotic system based on synchronised Master–Slave Chua's circuits has been used as a chaotic true random number generator (CTRNG. Chaotic systems present unpredictable and complex behaviour. This characteristic, together with the dependence on the initial conditions as well as the tolerance of the circuit components, make CTRNGs ideal for cryptography. In the proposed system, the transmitter mixes an input image with chaotic noise produced by a CTRNG. Using thresholding techniques, the chaotic signal is converted to a true random bit sequence. The receiver must be able to reproduce exactly the same chaotic noise in order to subtract it from the received signal. This becomes possible with synchronisation between the two Chua's circuits: through the use of specific techniques, the trajectory of the Slave chaotic system can be bound to that of the Master circuit producing (almost identical behaviour. Additional blocks have been used in order to make the system highly parameterisable and robust against common attacks. The whole system is simulated in Matlab. Simulation results demonstrate satisfactory performance, as well as, robustness against cryptanalysis. The system works with both greyscale and colour jpg images.
Stego Optical Encryption Based on Chaotic Baker's Map Transformation
Hussain, Iqtadar; Gondal, Muhammad Asif
2014-06-01
In this article, an optical image encryption algorithm based on chaotic baker's map is presented. The stego-image is encrypted with the help of double random phase encoding algorithm and then produced disorder with the help of chaotic transformation. Security test shows that the reading of proposed algorithm is very close to the optimal values.
Chaotic Feature in the Light Curve of 3C 273
Institute of Scientific and Technical Information of China (English)
Lei Liu
2006-01-01
Some nonlinear dynamical techniques, including state-space reconstruction and correlation integral, are used to analyze the light curve of 3C 273. The result is compared with a chaotic model. The similarities between them suggest there is a low-dimension chaotic attractor in the light curve of 3C 273.
Nonlinear transient and chaotic interactions in disc brake squeal
Oberst, S.; Lai, J. C. S.
2015-04-01
In automotive disc-brake squeal, most numerical studies have been focussed on the prediction of unstable vibration modes in the frequency domain using the complex eigenvalue analysis. However, the magnitude of the positive real part of a complex eigenvalue is an unreliable indicator of squeal occurrence. Although nonlinearities have been shown to play a significant role in brake squeal, transient nonlinear time domain analyses have rarely been applied owing to high computational costs. Here the complex eigenvalue analysis, the direct steady-state analysis and the transient nonlinear time domain analysis are applied to an isotropic pad-on-disc finite element model representing a simple model of a brake system. While in this investigation, in-plane pad-mode instabilities are not detected by the complex eigenvalue analysis, the dissipated energy obtained by the direct steady-state analysis of the model subjected to harmonic contact pressure excitation is negative at frequencies of pad modes, indicating a potential for instabilities. Transient nonlinear time domain analysis of the pad and disc dynamics reveal that in-plane pad vibrations excite a dominant out-of-plane disc mode. For intermittently chaotic pad motion, the disc dynamics is quasi-periodic; and for chaotic motion of the pad, a toroidal attractor is found for the disc's out-of-plane motion. Nonlinear interactions between the pad and the disc highlight that different parts in a brake system display different dynamic behaviour and need to be analysed separately. The type II intermittency route to chaos could be the cause for the experimentally observed instantaneous mode squeal.
Chaotic Diffusion in the Gliese-876 Planetary System
Martí, J G; Beaugé, C
2016-01-01
Chaotic diffusion is supposed to be responsible for orbital instabilities in planetary systems after the dissipation of the protoplanetary disk, and a natural consequence of irregular motion. In this paper we show that resonant multi-planetary systems, despite being highly chaotic, not necessarily exhibit significant diffusion in phase space, and may still survive virtually unchanged over timescales comparable to their age.Using the GJ-876 system as an example, we analyze the chaotic diffusion of the outermost (and less massive) planet. We construct a set of stability maps in the surrounding regions of the Laplace resonance. We numerically integrate ensembles of close initial conditions, compute Poincar\\'e maps and estimate the chaotic diffusion present in this system. Our results show that, the Laplace resonance contains two different regions: an inner domain characterized by low chaoticity and slow diffusion, and an outer one displaying larger values of dynamical indicators. In the outer resonant domain, th...
Chaotic carrier pulse position modulation communication system and method
Abarbanel, Henry D. I.; Larson, Lawrence E.; Rulkov, Nikolai F.; Sushchik, Mikhail M.; Tsimring, Lev S.; Volkovskii, Alexander R.
2001-01-01
A chaotic carrier pulse position modulation communication system and method is disclosed. The system includes a transmitter and receiver having matched chaotic pulse regenerators. The chaotic pulse regenerator in the receiver produces a synchronized replica of a chaotic pulse train generated by the regenerator in the transmitter. The pulse train from the transmitter can therefore act as a carrier signal. Data is encoded by the transmitter through selectively altering the interpulse timing between pulses in the chaotic pulse train. The altered pulse train is transmitted as a pulse signal. The receiver can detect whether a particular interpulse interval in the pulse signal has been altered by reference to the synchronized replica it generates, and can therefore detect the data transmitted by the receiver. Preferably, the receiver predicts the earliest moment in time it can expect a next pulse after observation of at least two consecutive pulses. It then decodes the pulse signal beginning at a short time before expected arrival of a pulse.
Chaotic dynamics of a Chua's system with voltage controllability
Heo, Yun Seok; Jung, Jin Woo; Kim, Ji Man; Jo, Mun Kyu; Song, Han Jung
2012-04-01
This paper presents an integrated circuit oriented Chua's chaotic system with voltage controllability. The proposed chaotic system consists of an OTA (Operational Transconductance Amplifier)-based ground inductor, two passive capacitors, a MOS (Metal-Oxide-Semiconductor)-based active resistor and an OTA-based Chua's diode with negative nonlinearity. A SPICE (Simulation Program with Integrated Circuit Emphasis) circuit analysis using 0.5-µm CMOS (Complementary Metal-Oxide-Semiconductor) process parameters was performed for the chaotic dynamics, such as the time waveform and the attractor plot. We confirmed that the chaotic behaviors of the system could be controlled by using the gate voltage of the MOS-based active resistor. Also, various chaotic dynamics of the circuit were analyzed for various MOS sizes of the OTA in the Chua's diode.
Do the chaotic features of gait change in Parkinson's disease?
Sarbaz, Yashar; Towhidkhah, Farzad; Jafari, Ayyoob; Gharibzadeh, Shahriar
2012-08-21
Some previous studies have focused on chaotic properties of Parkinson's disease (PD). It seems that considering PD from dynamical systems perspective is a relevant method that may lead to better understanding of the disease. There is some ambiguity about chaotic nature in PD symptoms and normal behaviour. Some studies claim that normal gait has somehow a chaotic behaviour and disturbed gait in PD has decreased chaotic nature. However, it is worth noting that the basis of this idea is the difference of fractal behaviour in gait of normal and PD patients, which is concluded from Long Range Correlation (LRC) indices. Our primary calculations show that a large number of normal persons and patients have similar LRC. It seems that chaotic studies on PD need a different view. Because of short time recording of symptoms, accurate calculation of chaotic features is tough. On the other hand, long time recording of symptoms is experimentally difficult. In this research, we have first designed a physiologically plausible model for normal and PD gait. Then, after validating the model with neural network classifier, we used the model for extracting long time simulation of stride in normal and PD persons. These long time simulations were then used for calculating the chaotic features of gait. According to change of phase space behaviour and alteration of three largest lyapunov exponents, it was observed that simulated normal persons act as chaotic systems in stride production, but simulated PD does not have chaotic dynamics and is stochastic. Based on our results, it may be claimed that normal gait has chaotic nature which is disturbed in PD state. Surely, long time real recordings from gait signal in normal persons and PD patients are necessary to warranty this hypothesis.
Chaotic Diffusion of Resonant Kuiper Belt Objects
Tiscareno, Matthew S
2008-01-01
We carried out extensive numerical orbit integrations to probe the long-term chaotic dynamics of the two strongest mean motion resonances of Neptune in the Kuiper belt, the 3:2 (Plutinos) and 2:1 (Twotinos). Our primary results include a computation of the relative volumes of phase space characterized by large- and small-resonance libration amplitudes, and maps of resonance stability measured by mean chaotic diffusion rate. We find that Neptune's 2:1 resonance has weaker overall long-term stability than the 3:2 -- only 15% of Twotinos are projected to survive for 4 Gyr, compared to 28% of Plutinos. We find that Pluto has only a modest effect, causing a ~4% decrease in the Plutino population that survives to 4 Gyr. Given current observational estimates, we conclude that the primordial populations of Plutinos and Twotinos formerly made up more than half the population of the classical and resonant Kuiper Belt. We also conclude that Twotinos were originally nearly as numerous as Plutinos, consistent with models ...
Parameter estimation methods for chaotic intercellular networks.
Mariño, Inés P; Ullner, Ekkehard; Zaikin, Alexey
2013-01-01
We have investigated simulation-based techniques for parameter estimation in chaotic intercellular networks. The proposed methodology combines a synchronization-based framework for parameter estimation in coupled chaotic systems with some state-of-the-art computational inference methods borrowed from the field of computational statistics. The first method is a stochastic optimization algorithm, known as accelerated random search method, and the other two techniques are based on approximate Bayesian computation. The latter is a general methodology for non-parametric inference that can be applied to practically any system of interest. The first method based on approximate Bayesian computation is a Markov Chain Monte Carlo scheme that generates a series of random parameter realizations for which a low synchronization error is guaranteed. We show that accurate parameter estimates can be obtained by averaging over these realizations. The second ABC-based technique is a Sequential Monte Carlo scheme. The algorithm generates a sequence of "populations", i.e., sets of randomly generated parameter values, where the members of a certain population attain a synchronization error that is lesser than the error attained by members of the previous population. Again, we show that accurate estimates can be obtained by averaging over the parameter values in the last population of the sequence. We have analysed how effective these methods are from a computational perspective. For the numerical simulations we have considered a network that consists of two modified repressilators with identical parameters, coupled by the fast diffusion of the autoinducer across the cell membranes.
Chaotic synchronization of two complex nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Mahmoud, Gamal M. [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)], E-mail: gmahmoud@aun.edu.eg; Mahmoud, Emad E. [Department of Mathematics, Faculty of Science, Sohag University (Egypt)], E-mail: emad_eluan@yahoo.com; Farghaly, Ahmed A. [Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516 (Egypt)], E-mail: ahmed_1_66@yahoo.com; Aly, Shaban A. [Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71511 (Egypt)], E-mail: shhaly12@yahoo.com
2009-12-15
Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing's oscillators. Physica A 2001;292:193-206], a system of periodically forced complex Duffing's oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schroedinger equation has also been pointed out. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.
Chaotic Image Encryption of Regions of Interest
Xiao, Di; Fu, Qingqing; Xiang, Tao; Zhang, Yushu
Since different regions of an image have different importance, therefore only the important information of the image regions, which the users are really interested in, needs to be encrypted and protected emphatically in some special multimedia applications. However, the regions of interest (ROI) are always some irregular parts, such as the face and the eyes. Assuming the bulk data in transmission without being damaged, we propose a chaotic image encryption algorithm for ROI. ROI with irregular shapes are chosen and detected arbitrarily. Then the chaos-based image encryption algorithm with scrambling, S-box and diffusion parts is used to encrypt the ROI. Further, the whole image is compressed with Huffman coding. At last, a message authentication code (MAC) of the compressed image is generated based on chaotic maps. The simulation results show that the encryption algorithm has a good security level and can resist various attacks. Moreover, the compression method improves the storage and transmission efficiency to some extent, and the MAC ensures the integrity of the transmission data.
On closure parameter estimation in chaotic systems
Directory of Open Access Journals (Sweden)
J. Hakkarainen
2012-02-01
Full Text Available Many dynamical models, such as numerical weather prediction and climate models, contain so called closure parameters. These parameters usually appear in physical parameterizations of sub-grid scale processes, and they act as "tuning handles" of the models. Currently, the values of these parameters are specified mostly manually, but the increasing complexity of the models calls for more algorithmic ways to perform the tuning. Traditionally, parameters of dynamical systems are estimated by directly comparing the model simulations to observed data using, for instance, a least squares approach. However, if the models are chaotic, the classical approach can be ineffective, since small errors in the initial conditions can lead to large, unpredictable deviations from the observations. In this paper, we study numerical methods available for estimating closure parameters in chaotic models. We discuss three techniques: off-line likelihood calculations using filtering methods, the state augmentation method, and the approach that utilizes summary statistics from long model simulations. The properties of the methods are studied using a modified version of the Lorenz 95 system, where the effect of fast variables are described using a simple parameterization.
Self-pulsing effect in chaotic scattering
Energy Technology Data Exchange (ETDEWEB)
Jung, C [Centro de Ciencias FIsicas, Universidad Nacional Autonoma de Mexico, Cuernavaca, Morelos (Mexico); MejIa-Monasterio, C [Centro de Ciencias FIsicas, Universidad Nacional Autonoma de Mexico, Cuernavaca, Morelos (Mexico); Merlo, O [Institut fuer Physik der Universitaet Basel, Basel (Switzerland); Seligman, T H [Centro de Ciencias FIsicas, Universidad Nacional Autonoma de Mexico, Cuernavaca, Morelos (Mexico)
2004-05-01
We study the quantum and classical scattering of Hamiltonian systems whose chaotic saddle is described by binary or ternary horseshoes. We are interested in situations for which a stable island, associated with the inner fundamental periodic orbit of the system exists and is large, but chaos around this island is well developed. Such situations are quite common as they correspond typically to the near-integrable domain in the transition from integrable to chaotic scattering. Both classical and quantum dynamics are analysed and in both cases, the most surprising effect is a periodic response to an incoming wave packet. The period of this self-pulsing effect or scattering echoes coincides with the mean period, by which the scattering trajectories rotate around the stable orbit. This period of rotation is directly related to the development stage of the underlying horseshoe. Therefore the predicted echoes will provide experimental access to topological information. We numerically test these results in kicked one-dimensional models and in open billiards.
Light matter interaction in chaotic resonators
Liu, Changxu
2016-05-11
Chaos is a complex dynamics with exponential sensitivity to the initial conditions. Since the study of three-body problem by Henri Poincare, chaos has been extensively studied in many systems, ranging from electronics to fluids, brains and more recently photonics. Chaos is a ubiquitous phenomenon in Nature, from the gigantic oceanic waves to the disordered scales of white beetles at nanoscale. The presence of chaos is often unwanted in applications, as it introduces unpredictability,which makes it difficult to predict or explain experimental results. Inspired by how chaos permeates the natural world, this thesis investigates on how the interaction between light and chaotic structure can enhance the performance of photonics devices. With a proper design of the lighter-mater interaction in chaotic resonators, I illustrate how chaos can be used to enhance the ability of an optical cavity to store electromagnetic energy, realize a blackbody system composed of gold nanoparticles, localize light beyond the diffraction limit and control the phase transition of super-radiance.
Jung, Jinwoo; Lee, Jewon; Song, Hanjung
2011-03-01
This paper presents a fully integrated circuit implementation of an operational amplifier (op-amp) based chaotic neuron model with a bipolar output function, experimental measurements, and analyses of its chaotic behavior. The proposed chaotic neuron model integrated circuit consists of several op-amps, sample and hold circuits, a nonlinear function block for chaotic signal generation, a clock generator, a nonlinear output function, etc. Based on the HSPICE (circuit program) simulation results, approximated empirical equations for analyses were formulated. Then, the chaotic dynamical responses such as bifurcation diagrams, time series, and Lyapunov exponent were calculated using these empirical equations. In addition, we performed simulations about two chaotic neuron systems with four synapses to confirm neural network connections and got normal behavior of the chaotic neuron such as internal state bifurcation diagram according to the synaptic weight variation. The proposed circuit was fabricated using a 0.8-μm single poly complementary metal-oxide semiconductor technology. Measurements of the fabricated single chaotic neuron with ± 2.5 V power supplies and a 10 kHz sampling clock frequency were carried out and compared with the simulated results.
Chen, Diyi; Zhang, Runfan; Sprott, J C; Chen, Haitao; Ma, Xiaoyi
2012-06-01
In this paper, we focus on the synchronization between integer-order chaotic systems and a class of fractional-order chaotic system using the stability theory of fractional-order systems. A new sliding mode method is proposed to accomplish this end for different initial conditions and number of dimensions. More importantly, the vector controller is one-dimensional less than the system. Furthermore, three examples are presented to illustrate the effectiveness of the proposed scheme, which are the synchronization between a fractional-order Chen chaotic system and an integer-order T chaotic system, the synchronization between a fractional-order hyperchaotic system based on Chen's system and an integer-order hyperchaotic system, and the synchronization between a fractional-order hyperchaotic system based on Chen's system and an integer-order Lorenz chaotic system. Finally, numerical results are presented and are in agreement with theoretical analysis.
A non-linear discrete transform for pattern recognition of discrete chaotic systems
Karanikas, C
2003-01-01
It is shown, by an invertible non-linear discrete transform that any finite sequence or any collection of strings of any length can be presented as a random walk on trees. These transforms create the mathematical background for coding any information, for exploring its local variability and diversity. With the underlying computational algorithms, with several examples and applications we propose that these transforms can be used for pattern recognition of immune type. In other words we propose a mathematical platform for detecting self and non-self strings of any alphabet, based on a negative selection algorithms, for scouting data's periodicity and self-similarity and for measuring the diversity of chaotic strings with fractal dimension methods. In particular we estimate successfully the entropy and the ratio of chaotic data with self similarity. Moreover we give some applications of a non-linear denoising filter.
Chaotic cold accretion on to black holes
Gaspari, M.; Ruszkowski, M.; Oh, S. Peng
2013-07-01
Bondi theory is often assumed to adequately describe the mode of accretion in astrophysical environments. However, the Bondi flow must be adiabatic, spherically symmetric, steady, unperturbed, with constant boundary conditions. Using 3D adaptive mesh refinement simulations, linking the 50 kpc to the sub-parsec (sub-pc) scales over the course of 40 Myr, we systematically relax the classic assumptions in a typical galaxy hosting a supermassive black hole. In the more realistic scenario, where the hot gas is cooling, while heated and stirred on large scales, the accretion rate is boosted up to two orders of magnitude compared with the Bondi prediction. The cause is the non-linear growth of thermal instabilities, leading to the condensation of cold clouds and filaments when tcool/tff ≲ 10. The clouds decouple from the hot gas, `raining' on to the centre. Subsonic turbulence of just over 100 km s-1 (M > 0.2) induces the formation of thermal instabilities, even in the absence of heating, while in the transonic regime turbulent dissipation inhibits their growth (tturb/tcool ≲ 1). When heating restores global thermodynamic balance, the formation of the multiphase medium is violent, and the mode of accretion is fully cold and chaotic. The recurrent collisions and tidal forces between clouds, filaments and the central clumpy torus promote angular momentum cancellation, hence boosting accretion. On sub-pc scales the clouds are channelled to the very centre via a funnel. In this study, we do not inject a fixed initial angular momentum, though vorticity is later seeded by turbulence. A good approximation to the accretion rate is the cooling rate, which can be used as subgrid model, physically reproducing the boost factor of 100 required by cosmological simulations, while accounting for the frequent fluctuations. Since our modelling is fairly general (turbulence/heating due to AGN feedback, galaxy motions, mergers, stellar evolution), chaotic cold accretion may be common in
Passive control of chaotic system with multiple strange attractors
Institute of Scientific and Technical Information of China (English)
Song Yun-Zhong; Zhao Guang-Zhou; Qi Dong-Lian
2006-01-01
In this paper we present a new simple controller for a chaotic system, that is, the Newton-Leipnik equation with two strange attractors: the upper attractor (UA) and the lower attractor (LA). The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form.Using a passive method, we prove the stability of a closed-loop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, separately: the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intra-attractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one,and the inter-attractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.
Dynamics of Transiently Chaotic Neural Network and Its Application to Optimization
Institute of Scientific and Technical Information of China (English)
YANG Li-Jiang; CHEN Tian-Lun; HUANG Wu-Qun
2001-01-01
Through adding a nonlinear self-feedback term in the evolution equations of neural network, we introduced a transiently chaotic neural network model. In order to utilize the transiently chaotic dynamics mechanism in optimization problem efficiently, we have analyzed the dynamical procedure of the transiently chaotic neural network rnodel and studied the function of the crucial bifurcation parameter which governs the chaotic behavior of the system. Based on the dynamical analysis of the transiently chaotic neural network model, chaotic annealing algorithm is also examined and improved. As an example, we applied chaotic annealing method to the traveling salesman problem and obtained good results.``
Efficient chaotic based satellite power supply subsystem
Energy Technology Data Exchange (ETDEWEB)
Ramos Turci, Luiz Felipe [Technological Institute of Aeronautics (ITA), Sao Jose dos Campos, SP (Brazil)], E-mail: felipeturci@yahoo.com.br; Macau, Elbert E.N. [National Institute of Space Research (Inpe), Sao Jose dos Campos, SP (Brazil)], E-mail: elbert@lac.inpe.br; Yoneyama, Takashi [Technological Institute of Aeronautics (ITA), Sao Jose dos Campos, SP (Brazil)], E-mail: takashi@ita.br
2009-10-15
In this work, we investigate the use of the Dynamical System Theory to increase the efficiency of the satellite power supply subsystems. The core of a satellite power subsystem relies on its DC/DC converter. This is a very nonlinear system that presents a multitude of phenomena ranging from bifurcations, quasi-periodicity, chaos, coexistence of attractors, among others. The traditional power subsystem design techniques try to avoid these nonlinear phenomena so that it is possible to use linear system theory in small regions about the equilibrium points. Here, we show that more efficiency can be drawn from a power supply subsystem if the DC/DC converter operates in regions of high nonlinearity. In special, if it operates in a chaotic regime, is has an intrinsic sensitivity that can be exploited to efficiently drive the power subsystem over high ranges of power requests by using control of chaos techniques.
Hybrid Monte Carlo with Chaotic Mixing
Kadakia, Nirag
2016-01-01
We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum distribution, and due to its mixing properties, exhibits sample-to-sample autocorrelations that decay far faster than those in the traditional hybrid Monte Carlo algorithm. We test the methods on distributions of varying correlation structure, finding that the proposed technique produces superior covariance estimates, is less reliant on step-size tuning, and can even function with sparse or no momentum re-sampling. The method presented here is promising for more general distributions, such as those that arise in Bayesian learning of artificial neural networks and in the state and parameter estimation of dynamical systems.
Chaotic inflation in higher derivative gravity theories
Myrzakul, Shynaray; Sebastiani, Lorenzo
2015-01-01
In this paper, we investigate chaotic inflation from scalar field subjected to potential in the framework of $f(R^2, P, Q)$-gravity, where we add a correction to Einstein's gravity based on a function of the square of the Ricci scalar $R^2$, the contraction of the Ricci tensor $P$, and the contraction of the Riemann tensor $Q$. The Gauss-Bonnet case is also discussed. We give the general formalism of inflation, deriving the slow-roll parameters, the $e$-folds number, and the spectral indexes. Several explicit examples are furnished, namely we will consider the cases of massive scalar field and scalar field with quartic potential and some power-law function of the curvature invariants under investigation in the gravitational action of the theory. Viable inflation according with observations is analyzed.
Chaotic Behavior in a Switched Dynamical System
Directory of Open Access Journals (Sweden)
Fatima El Guezar
2008-01-01
Full Text Available We present a numerical study of an example of piecewise linear systems that constitute a class of hybrid systems. Precisely, we study the chaotic dynamics of the voltage-mode controlled buck converter circuit in an open loop. By considering the voltage input as a bifurcation parameter, we observe that the obtained simulations show that the buck converter is prone to have subharmonic behavior and chaos. We also present the corresponding bifurcation diagram. Our modeling techniques are based on the new French native modeler and simulator for hybrid systems called Scicos (Scilab connected object simulator which is a Scilab (scientific laboratory package. The followed approach takes into account the hybrid nature of the circuit.
Chaotic behaviour of high Mach number flows
Varvoglis, H.; Ghosh, S.
1985-01-01
The stability of the super-Alfvenic flow of a two-fluid plasma model with respect to the Mach number and the angle between the flow direction and the magnetic field is investigated. It is found that, in general, a large scale chaotic region develops around the initial equilibrium of the laminar flow when the Mach number exceeds a certain threshold value. After reaching a maximum the size of this region begins shrinking and goes to zero as the Mach number tends to infinity. As a result high Mach number flows in time independent astrophysical plasmas may lead to the formation of 'quasi-shocks' in the presence of little or no dissipation.
Chaotic motion in the Jovian atmosphere
Pirraglia, Joseph
1986-01-01
Strong nonlinear interactions among unstable waves and the mean flow occur in a simplified quasigeostrophic spectral model of the upper troposphere of Jupiter. The upper boundary of the layer inhibits vertical motion while at the lower boundary perturbations of the potential temperature are not permitted. On an infinite beta plane the forced flow of alternating zones of prograde and retrograde zonal winds, decreasing with height, are linearly unstable and it is shown that the nonlinear terms stabilize the flow by bounding the growth of the eddies. Explicit viscosity terms are not needed. This does not imply that energy would not cascade to the small scale flow but suggests that the nature of the large scale flow is independent of the viscosity at small scales. Numerical time integration shows the flow to be chaotic but, in some cases, with transient propagating features and meandering zonal flow.
Cryptography based on spatial chaotic system
Sun, Fuyan; Lü, Zongwang
2010-08-01
Encryption of images is different from that of texts due to some intrinsic features of images such as bulk data capacity and high redundancy, which is generally difficult to handle by traditional methods. This paper proposes a new spatial chaos system(SCS), which is investigated by conducting FIPS 140-1 statistic test, and is especially useful for encryption of digital images. It is shown how to adapt a two dimensional(2D) ergodic matrix obtained from SCS to permute the positions of image pixels and confuse the relationship between the cipher image and plain image simultaneously. Experimental results show that the performance and security of the proposed cryptographic system are better than those of existing lower dimensional chaotic cryptographic systems.
Chaotic Disintegration of the Inner Solar System
Batygin, Konstantin; Holman, Mathew J
2014-01-01
On timescales that greatly exceed an orbital period, typical planetary orbits evolve in a stochastic yet stable fashion. On even longer timescales, however, planetary orbits can spontaneously transition from bounded to unbound chaotic states. Large-scale instabilities associated with such behavior appear to play a dominant role in shaping the architectures of planetary systems, including our own. Here we show how such transitions are possible, focusing on the specific case of the long-term evolution of Mercury. We develop a simple analytical model for Mercury's dynamics and elucidate the origins of its short term stochastic behavior as well as of its sudden progression to unbounded chaos. Our model allows us to estimate the timescale on which this transition is likely to be triggered, i.e. the dynamical lifetime of the Solar System as we know it. The formulated theory is consistent with the results of numerical simulations and is broadly applicable to extrasolar planetary systems dominated by secular interact...
Chiral scars in chaotic Dirac fermion systems.
Xu, Hongya; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2013-02-08
Do relativistic quantum scars in classically chaotic systems possess unique features that are not shared by nonrelativistic quantum scars? We report a class of relativistic quantum scars in massless Dirac fermion systems whose phases return to the original values or acquire a 2π change only after circulating twice about some classical unstable periodic orbits. We name such scars chiral scars, the successful identification of which has been facilitated tremendously by our development of an analytic, conformal-mapping-based method to calculate an unprecedentedly large number of eigenstates with high accuracy. Our semiclassical theory indicates that the physical origin of chiral scars can be attributed to a combined effect of chirality intrinsic to massless Dirac fermions and the geometry of the underlying classical orbit.
Chaotic inflation in higher derivative gravity theories
Energy Technology Data Exchange (ETDEWEB)
Myrzakul, Shynaray; Myrzakulov, Ratbay; Sebastiani, Lorenzo [Eurasian National University, Department of General and Theoretical Physics, Eurasian Center for Theoretical Physics, Astana (Kazakhstan)
2015-03-01
In this paper, we investigate chaotic inflation from a scalar field subjected to a potential in the framework of f(R{sup 2}, P, Q)-gravity, where we add a correction to Einstein's gravity based on a function of the square of the Ricci scalar R{sup 2}, the contraction of the Ricci tensor P, and the contraction of the Riemann tensor Q. The Gauss-Bonnet case is also discussed. We give the general formalism of inflation, deriving the slow-roll parameters, the e-fold number, and the spectral indices. Several explicit examples are furnished; namely, we will consider the cases of a massive scalar field and a scalar field with quartic potential and some power-law function of the curvature invariants under investigation in the gravitational action of the theory. A viable approach to inflation according with observations is analyzed. (orig.)
Chaotic Motions of F-Ring Shepherds
Goldreich, P; Goldreich, Peter; Rappaport, Nicole
2002-01-01
Recent HST images of the Saturnian satellites Prometheus and Pandora show that their longitudes deviate from predictions of ephemerides based on Voyager images. Currently Prometheus is lagging and Pandora leading these predictions by somewhat more than 20 degrees. We show that these discrepancies are fully accounted for by gravitational interactions between the two satellites. These peak every 24.8 days at conjunctions and excite chaotic perturbations. The Lyapunov exponent for the Prometheus-Pandora system is of order 0.35 inverse years for satellite masses based on a nominal density of 1.3 gm/cm^3. Interactions are strongest when the orbits come closest together. This happens at intervals of 6.2 years when their apses are anti-aligned. In this context we note the sudden changes of opposite signs in the mean motions of Prometheus and Pandora at the end of 2000 occured shortly after their apsidal lines were anti-aligned.
A New Angle on Chaotic Inflation
Bachlechner, Thomas C; Frazer, Jonathan; McAllister, Liam
2014-01-01
N-flation is a radiatively stable scenario for chaotic inflation in which the displacements of $N \\gg 1$ axions with decay constants $f_1 \\le \\ldots \\le f_N < M_P$ lead to a super-Planckian effective displacement equal to the Pythagorean sum $f_{Py}$ of the $f_i$. We show that mixing in the axion kinetic term generically leads to the phenomenon of kinetic alignment, allowing for effective displacements as large as $\\sqrt{N} f_{N} \\ge f_{Py}$, even if $f_1, \\ldots, f_{N-1}$ are arbitrarily small. At the level of kinematics, the necessary alignment occurs with very high probability, because of eigenvector delocalization. We present conditions under which inflation can take place along an aligned direction. Our construction sharply reduces the challenge of realizing N-flation in string theory.
Dynamics of quantum trajectories in chaotic systems
Wisniacki, D A; Benito, R M
2003-01-01
Quantum trajectories defined in the de Broglie--Bohm theory provide a causal way to interpret physical phenomena. In this Letter, we use this formalism to analyze the short time dynamics induced by unstable periodic orbits in a classically chaotic system, a situation in which scars are known to play a very important role. We find that the topologies of the quantum orbits are much more complicated than that of the scarring and associated periodic orbits, since the former have quantum interference built in. Thus scar wave functions are necessary to analyze the corresponding dynamics. Moreover, these topologies imply different return routes to the vicinity of the initial positions, and this reflects in the existence of different contributions in each peak of the survival probability function.
Signals of chaotic behavior in PMMA
Hacinliyan, A; Sahin, G; Akin, G
2003-01-01
The time evolution of the current passing through PMMA polymer thin films under 10 V at 23 deg. C (296 K) was sampled at intervals ranging from 1 to 20 s. The data showed chaotic behavior in the context of pinned charge density waves [Phys. Rev. B 41 (1990) 11522]. The resultant time series has been analyzed by means of TISEAN, time series analysis software [The TISEAN package CHAOS 9 (1999) 413]. The analysis has revealed a positive maximal Lyapunov exponent. This is also corroborated by a calculation of the fractal dimension and application of the Kaplan-Yorke conjecture. In the analysis two widely separated time scales have been observed; the first zero crossing of the correlation function at 8380 s and the first marked minimum of the average mutual information at 40 s.
Spectral properties of dissipative chaotic quantum maps.
Braun, Daniel
1999-09-01
I examine spectral properties of a dissipative chaotic quantum map with the help of a recently discovered semiclassical trace formula. I show that in the presence of a small amount of dissipation the traces of any finite power of the propagator of the reduced density matrix, and traces of its classical counterpart, the Frobenius-Perron operator, are identical in the limit of variant Planck's over 2pi -->0. Numerically I find that even for finite variant Planck's over 2pi the agreement can be very good. This holds in particular if the classical phase space contains a strange attractor, as long as one stays clear of bifurcations. Traces of the quantum propagator for iterations of the map agree well with the corresponding traces of the Frobenius-Perron operator if the classical dynamics is dominated by a strong point attractor. (c) 1999 American Institute of Physics.
Chaotic itinerancy and its roles in cognitive neurodynamics.
Tsuda, Ichiro
2015-04-01
Chaotic itinerancy is an autonomously excited trajectory through high-dimensional state space of cortical neural activity that causes the appearance of a temporal sequence of quasi-attractors. A quasi-attractor is a local region of weakly convergent flows that represent ordered activity, yet connected to divergent flows representing disordered, chaotic activity between the regions. In a cognitive neurodynamic aspect, quasi-attractors represent perceptions, thoughts and memories, chaotic trajectories between them with intelligent searches, such as history-dependent trial-and-error via exploration, and itinerancy with history-dependent sequences in thinking, speaking and writing.
Modified scaling function projective synchronization of chaotic systems
Institute of Scientific and Technical Information of China (English)
Xu Yu-Hua; Zhou Wu-Neng; Fang Jian-An
2011-01-01
This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point,a periodic orbit,or even a chaotic attractor in the phase space. Based on LaSa11e's invariance set principle,the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.
Designing for chaos: applications of chaotic advection at the microscale.
Stremler, Mark A; Haselton, F R; Aref, Hassan
2004-05-15
Chaotic advection can play an important role in efficient microfluidic mixers. We discuss a design paradigm that exploits chaotic advection and illustrate by two recent examples, namely enhancing gene expression profiling and constructing an in-line microfluidic mixing channel, how application of this paradigm has led to successful micromixers. We suggest that 'designing for chaos', that is, basing practical mixer design on chaotic advection analysis, is a promising approach to adopt in this developing field which otherwise has little to guide it and is constrained by issues of scale and manufacturability.
Random symmetry breaking and freezing in chaotic networks.
Peleg, Y; Kinzel, W; Kanter, I
2012-09-01
Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a nonchaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped oscillators is shown to present chaotic dynamics while the sign amplitude of each damped oscillator is randomly frozen. This phenomenon of random broken global symmetry of the network simultaneous with random freezing of each degree of freedom is accompanied by the existence of exponentially many randomly frozen chaotic attractors with the size of the network. Results are exemplified by a network of modified Duffing oscillators with infinite range pseudoinverse delayed interactions.