scholarly journals Synchronized Attractors and Phase Entrained with Cavity Loss of the Coupled Laser’s Map

2022 ◽  
Author(s):  
Abdul Abdul ◽  
Altaf Ur Rahman ◽  
Chen Minjing ◽  
Jehan Akbar ◽  
Farhan Saif ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Symmetry Breaking ◽  
Coupling Strength ◽  
Strange Attractors ◽  
Chaotic Attractors ◽  
Cavity Loss ◽  
Numerical Studies ◽  
Coupled Maps ◽  
Basin Boundaries

The laser differential equations are used to transform them into identical coupled maps. Valuable results are deduced during analytical and numerical studies on cavity loss. Phase and spatiotemporal synchronized attractors are observed via quasi-chaos under a certain range of controlling parameters, and symmetry breaking of chaotic attractors due to collision with their basin boundaries, and transpire differently from the previous attractors. During the numerical simulation, it is found that the sequence of repeated strange attractors if the coupling strength further increases, which are orthogonal mirror images (the dynamics of the system is the same at different values of controlling parameters). Moreover, it can help us to predict future problems and their solutions based on current issues, if we develop this model in more general.

On the Influence of the Coupling Strength among Chua’s Circuits on the Structure of Their Hyper-Chaotic Attractors

2016 ◽  
Vol 26 (07) ◽  
pp. 1650115 ◽  
Author(s):  
Sven Freud ◽  
Rainer Plaga ◽  
Ralph Breithaupt
Keyword(s):  
Significant Influence ◽  
Coupling Strength ◽  
Strange Attractor ◽  
Chaotic Dynamics ◽  
Strange Attractors ◽  
Chaotic Attractors ◽  
Physical Unclonable Functions ◽  
Coupling Strengths ◽  
Probability Of Presence ◽  
Random Fluctuations

The hyper-chaotic strange attractor of systems of four Chua’s circuits that are mutually coupled by three strong and three weak couplings is studied, both experimentally and via simulation. A new metric to compare strange attractors is presented. It is found that the strength of the couplings between circuits have a complex and determining influence on the probability for the presence of a trajectory within their attractors. This influence is strictly local, i.e. the probability of the presence of the trajectories is determined by the coupling strength to the directly adjacent circuits and independent of the coupling strengths among other circuits. Fluctuations in the properties of Chua’s circuits due to random fluctuations during the production of its components have a significant influence on the probability of presence of the attractor’s trajectories that could be qualitatively, but not quantitatively, modeled by our simulation. The consequences of these results for the possibility to construct “physical unclonable functions” as networks of Chua’s circuits with a hyper-chaotic dynamics are discussed.

Nonlinear Dynamics and Application of the Four Dimensional Autonomous Hyper-Chaotic System

2014 ◽  
Author(s):  
Ge Kai ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Differential Equations ◽  
Chaotic System ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Phase Portraits ◽  
State Variables ◽  
Chaotic Motions ◽  
Finance System

In this paper, we establish a dynamic model of the hyper-chaotic finance system which is composed of four sub-blocks: production, money, stock and labor force. We use four first-order differential equations to describe the time variations of four state variables which are the interest rate, the investment demand, the price exponent and the average profit margin. The hyper-chaotic finance system has simplified the system of four dimensional autonomous differential equations. According to four dimensional differential equations, numerical simulations are carried out to find the nonlinear dynamics characteristic of the system. From numerical simulation, we obtain the three dimensional phase portraits that show the nonlinear response of the hyper-chaotic finance system. From the results of numerical simulation, it is found that there exist periodic motions and chaotic motions under specific conditions. In addition, it is observed that the parameter of the saving has significant influence on the nonlinear dynamical behavior of the four dimensional autonomous hyper-chaotic system.

Mulit-Pulse Orbits and Chaotic Motion of Composite Laminated Plates

2008 ◽  
Author(s):  
Xiangying Guo ◽  
Wei Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Numerical Simulation ◽  
Normal Form ◽  
Differential Equations ◽  
Thin Plate ◽  
Equations Of Motion ◽  
Laminated Plates ◽  
Phase Method ◽  
Rectangular Thin Plate ◽  
Partial Differential ◽  
Chaotic Motions

This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy’s three-order shear deformation plate theory and the model of the von Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton’s principle. Then, using the second-order Galerkin discretization approach, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1:1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the energy phase method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation. The results of numerical simulation also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.

scholarly journals Low Model Analysis and Synchronous Simulation of the Wave Mechanics

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wenyuan Duan ◽  
Heyuan Wang ◽  
Meng Kan
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Chaotic System ◽  
Invariant Set ◽  
Positive Definite ◽  
Chaotic Attractors ◽  
Wave Mechanics ◽  
Wave Dynamics ◽  
Simulation Results ◽  
Positive Invariant Set

The dynamic behavior of a chaotic system in the internal wave dynamics and the problem of the tracing and synchronization are investigated, and the numerical simulation is carried out in this paper. The globally exponentially attractive set and positive invariant set of the chaotic system are studied via constructing the positive definite and radial unbounded Lyapunov function. There are no equilibrium positions, periodic solutions, quasi-period motions, wandering recovering motions, and other chaotic attractors of the system out of the globally exponentially attractive set. Strange attractors can only locate in the globally exponentially attractive set. A feedback controller is designed for the chaotic system to realize the control of the unstable point. The second method of Lyapunov is used to discuss theoretically the rationality of the design of the controller. The driving-response synchronization method is used to realize the globally exponential synchronization. The numerical simulation is carried out by MATLAB software, and the simulation results show that the method is effective.

Various Types of Coexisting Attractors in a New 4D Autonomous Chaotic System

2017 ◽  
Vol 27 (09) ◽  
pp. 1750142 ◽  
Author(s):  
Qiang Lai ◽  
Akif Akgul ◽  
Xiao-Wen Zhao ◽  
Huiqin Pei
Keyword(s):  
Numerical Simulation ◽  
Dynamic Behavior ◽  
Chaotic System ◽  
Limit Cycles ◽  
Electronic Circuit ◽  
Strange Attractors ◽  
Bifurcation Diagrams ◽  
Coexisting Attractors ◽  
Signum Function ◽  
Multiple Coexisting Attractors

An unique 4D autonomous chaotic system with signum function term is proposed in this paper. The system has four unstable equilibria and various types of coexisting attractors appear. Four-wing and four-scroll strange attractors are observed in the system and they will be broken into two coexisting butterfly attractors and two coexisting double-scroll attractors with the variation of the parameters. Numerical simulation shows that the system has various types of multiple coexisting attractors including two butterfly attractors with four limit cycles, two double-scroll attractors with a limit cycle, four single-scroll strange attractors, four limit cycles with regard to different parameters and initial values. The coexistence of the attractors is determined by the bifurcation diagrams. The chaotic and hyperchaotic properties of the attractors are verified by the Lyapunov exponents. Moreover, we present an electronic circuit to experimentally realize the dynamic behavior of the system.

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