Distribution of subcritical Hopf bifurcations and regular and chaotic attractors in optical bistable systems

1990 ◽  
Vol 41 (7) ◽  
pp. 3975-3984 ◽  
Author(s):  
Hu Gang ◽  
Cun-zheng Ning ◽  
H. Haken
Keyword(s):  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
Bistable Systems

A MODIFIED GENERALIZED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM

2009 ◽  
Vol 19 (06) ◽  
pp. 1931-1949 ◽  
Author(s):  
QIGUI YANG ◽  
KANGMING ZHANG ◽  
GUANRONG CHEN
Keyword(s):  
Special Form ◽  
Topological Structure ◽  
Complex Dynamics ◽  
Type System ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
Compound Structure ◽  
Two Parameters ◽  
First Time ◽  
New System

In this paper, a modified generalized Lorenz-type system is introduced, which is state-equivalent to a simple and special form, and is parameterized by two parameters useful for chaos turning and system classification. More importantly, based on the parameterized form, two classes of new chaotic attractors are found for the first time in the literature, which are similar but nonequivalent in topological structure. To further understand the complex dynamics of the new system, some basic properties such as Lyapunov exponents, Hopf bifurcations and compound structure of the attractors are analyzed and demonstrated with careful numerical simulations.

scholarly journals Dynamic Analysis of a Particle Motion System

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 7
Author(s):  
Ning Cui ◽  
Junhong Li
Keyword(s):  
Particle Motion ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
Equilibrium Stability ◽  
Dynamic Behaviors ◽  
Motion System ◽  
The Rich ◽  
Theoretical Analyses

This paper formulates a new particle motion system. The dynamic behaviors of the system are studied including the continuous dependence on initial conditions of the system’s solution, the equilibrium stability, Hopf bifurcation at the equilibrium point, etc. This shows the rich dynamic behaviors of the system, including the supercritical Hopf bifurcations, subcritical Hopf bifurcations, and chaotic attractors. Numerical simulations are carried out to verify theoretical analyses and to exhibit the rich dynamic behaviors.

Chaotic attractors formed using bistable systems

2004 ◽  
Vol 30 (7) ◽  
pp. 550-552
Author(s):  
Er. V. Kal’yanov
Keyword(s):  
Chaotic Attractors ◽  
Bistable Systems

A NEW CLASS OF CHAOTIC ATTRACTORS IN MURALI–LAKSHMANAN–CHUA CIRCUIT

2006 ◽  
Vol 16 (09) ◽  
pp. 2659-2670 ◽  
Author(s):  
ALI OKSASOGLU ◽  
QIUDONG WANG
Keyword(s):  
Limit Cycles ◽  
Short Pulse ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
Stable Limit ◽  
New Class ◽  
Chua Circuit ◽  
Rank One ◽  
Weakly Stable ◽  
Stable Limit Cycles

In this paper, we study the existence of a new class of chaotic attractors, namely the rank-one attractors, in the MLC (Murali–Lakshmanan–Chua) circuit [Murali et al., 1994] by numerical simulations based on a theory of rank-one maps developed in [Wang & Young, 2005]. With the guidance of the theory in [Wang & Young, 2005], weakly stable limit cycles, found through Hopf bifurcations and other numerical means, are subjected to periodic pulses with long relaxation periods to produce rank-one attractors. The periodic pulses are applied directly as an input. Periodic pulses have been used before in various schemes of chaos. However, for this scheme of creating rank-one attractors to work, the applied periodic pulses must have short pulse widths and long relaxation periods. This is one of the key components in creating this new class of chaotic attractors.

A novel 4D chaotic system with multistability: Dynamical analysis, circuit implementation, control design

2019 ◽  
Vol 33 (21) ◽  
pp. 1950240 ◽  
Author(s):  
Jian-Jun He ◽  
Bang-Cheng Lai
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Electronic Circuit ◽  
Period Doubling ◽  
Control Design ◽  
Critical Value ◽  
Dynamical Analysis ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
The Novel

The purpose of this work is to introduce a novel 4D chaotic system and investigate its multistability. The novel system has an unstable origin and two stable symmetrical hyperbolic equilibria. When the parameter increases across a critical value, the equilibria lose their stability and double Hopf bifurcations occur with the appearance of limit cycles. A pair of point, periodic, chaotic attractors are observed in the system from different initial values for given parameters. The chaos of the system is yielded via period-doubling bifurcation. A double-scroll chaotic attractor is numerically observed as well. By using the electronic circuit, the chaotic attractor of the system is realized. The control problem of the system is reported. An effective controller is designed to stabilize the system.

DYNAMIC RESPONSE AND NOISE SUSCEPTIBILITY OF c.w. BISTABLE SYSTEMS

1988 ◽  
Vol 49 (C2) ◽  
pp. C2-161-C2-164
Author(s):  
H. A. MacKENZIE ◽  
J. YOUNG ◽  
A. ILTAIF ◽  
J. HUGHES
Keyword(s):  
Dynamic Response ◽  
Bistable Systems ◽  
Noise Susceptibility

Visualization analysis on stretch-and-fold mechanism of chaotic attractors

2014 ◽  
Vol 1 ◽  
pp. 443-446
Author(s):  
Yutaka Shimada ◽  
Takuya Kobayashi ◽  
Tohru Ikeguchi ◽  
Kazuyuki Aihara
Keyword(s):  
Chaotic Attractors ◽  
Visualization Analysis

scholarly journals Stochastic resonance in periodically driven bistable systems subjected to anomalous diffusion

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
F. Naha Nzoupe ◽  
Alain M. Dikandé
Keyword(s):  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Planck Equation ◽  
Relevant Information ◽  
Periodic Signal ◽  
Signal To Noise ◽  
Periodically Driven ◽  
Loop Area ◽  
Bistable Systems ◽  
Noise Ratio

AbstractThe occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with an emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker–Planck equation describing the system dynamics, together with the corresponding Ito–Langevin equation, is formulated. In the linear response regime, analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived as quantifiers of stochastic resonance. These quantifiers are found to be strongly dependent on the parameters controlling the type of diffusion; in particular, the peak characterizing the signal-to-noise ratio occurs only in close ranges of parameters. Results introduce the relevant information that, taking into consideration the interactions of anomalous diffusive systems with a periodic signal, can provide a better understanding of the physics of stochastic resonance in bistable systems driven by periodic forces.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

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