Proximity to periodic windows in bifurcation diagrams as a gateway to coherence resonance in chaotic systems

2007 ◽  
Vol 76 (3) ◽  
Author(s):  
Marko Gosak ◽  
Matjaž Perc
Keyword(s):  
Chaotic Systems ◽  
Bifurcation Diagrams ◽  
Coherence Resonance

scholarly journals A new scheme of coupling and synchronizing low-dimensional dynamical systems

2021 ◽  
Vol 67 (2 Mar-Apr) ◽  
pp. 334
Author(s):  
U. Uriostegui Legorreta ◽  
E. S. Tututi Hernández ◽  
G. Arroyo-Correa
Keyword(s):  
Dynamical Systems ◽  
Chaotic Systems ◽  
Nonlinear Circuits ◽  
Bifurcation Diagrams ◽  
Partial Synchronization ◽  
Low Dimensionality ◽  
Low Dimensional ◽  
The Way

A different manner of study synchronization between chaotic systems is presented. This is done by using two different forced coupled nonlinear circuits. The way of coupling the systems under study is different from those used in the analysis of chaos in dynamical systems of low dimensionality. The study of synchronization and how to manipulate it, is carried out through the variation of the couplings by calculating the bifurcation diagrams. We observed that for rather larger values of the coupling between the circuits it is reached total synchronization, while for small values of the coupling it is obtained, in the best of the cases, partial synchronization.

A GENERALIZED 3-D FOUR-WING CHAOTIC SYSTEM

2009 ◽  
Vol 19 (11) ◽  
pp. 3841-3853 ◽  
Author(s):  
ZENGHUI WANG ◽  
GUOYUAN QI ◽  
YANXIA SUN ◽  
MICHAËL ANTONIE VAN WYK ◽  
BAREND JACOBUS VAN WYK
Keyword(s):  
Phase Diagrams ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Autonomous System ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
Bifurcation Diagrams ◽  
Basic Properties ◽  
New System

In this paper, several three-dimensional (3-D) four-wing smooth quadratic autonomous chaotic systems are analyzed. It is shown that these systems have similar features. A simpler and generalized 3-D continuous autonomous system is proposed based on these features which can be extended to existing 3-D four-wing chaotic systems by adding some linear and/or quadratic terms. The new system can generate a four-wing chaotic attractor with simple topological structures. Some basic properties of the new system is analyzed by means of Lyapunov exponents, bifurcation diagrams and Poincaré maps. Phase diagrams show that the equilibria are related to the existence of multiple wings.

scholarly journals Coherence resonance in chaotic systems

2001 ◽  
Vol 56 (3) ◽  
pp. 347-353 ◽  
Author(s):  
C Palenzuela ◽  
R Toral ◽  
C. R Mirasso ◽  
O Calvo ◽  
J. D Gunton
Keyword(s):  
Chaotic Systems ◽  
Coherence Resonance

Behavior Studies of Nonlinear Fractional-Order Dynamical Systems Using Bifurcation Diagram

2018 ◽  
pp. 166-189
Author(s):  
Karima Rabah
Keyword(s):  
Seventeenth Century ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
Bifurcation Diagrams ◽  
Science And Engineering ◽  
Differential Systems ◽  
The Past ◽  
Important Objective

Over the past decades, chaos has stimulated the interest of researchers due to its existence in different fields of science and engineering. The chaotic systems are characterized by their sensitivity to the initial conditions. This property makes the system unpredictable long term. Similar to the integer-order differential systems, fractional-order differential systems can exhibit chaotic behaviors. This type of system contains one or more elements of fractional order. The fractional calculus is recognized in the early seventeenth century but it has been widely applied in many fields and with intense growth just over the past decades. To avoid troubles arising from unusual behaviors of a chaotic system, chaos control has gained increasing attention in recent years. An important objective of a chaos controller is to suppress the chaotic oscillations completely or reduce them to the regular oscillations. The goal of this chapter is to present the evolution of chaotic systems in open and closed loop in function of their parameters and designing a controller using bifurcation diagrams.

scholarly journals Dynamical Analysis of a Novel 4-D Hyper-Chaotic System With One Non-Hyperbolic Equilibrium Point and Application in Secure Communication

2020 ◽  
Vol 9 (4) ◽  
pp. 74-99
Author(s):  
Pushali Trikha ◽  
Lone Seth Jahanzaib
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
The Novel ◽  
Bifurcation Diagrams ◽  
Dynamical Properties ◽  
Hyperbolic Equilibrium ◽  
Hyperbolic Equilibrium Point

In this article, a novel hyper-chaotic system has been introduced and its dynamical properties (i.e., phase plots, time series, lyapunov exponents, bifurcation diagrams, equilibrium points, Poincare sections, etc.) have been studied. Also, the novel chaotic systems have been synchronized using novel synchronization technique multi-switching compound difference synchronization and its application have been shown in the field of secure communication. Numerical simulations have been undertaken to validate the efficacy of the synchronization in secure communication.

COHERENCE RESONANCE OF THE NOISE-INDUCED MOTION ON THE WAY TO BREAKDOWN OF SYNCHRONIZATION IN CHAOTIC SYSTEMS

2003 ◽  
Vol 03 (02) ◽  
pp. L113-L120 ◽  
Author(s):  
A. G. BALANOV ◽  
N. B. JANSON ◽  
P. V. E. McCLINTOCK
Keyword(s):  
Noise Intensity ◽  
Chaotic Systems ◽  
Phase Synchronization ◽  
Coherence Resonance ◽  
Frequency Locking ◽  
Periodic Oscillations ◽  
Induced Motion ◽  
Natural Dynamics ◽  
The Way

We investigate the way in which noise destroys phase synchronization in chaotic systems. Two cases are considered: where the route to synchronization involves frequency locking; and where it occurs via a suppression of the natural dynamics. We show that, just as in the case of synchronization of periodic oscillations, noise induces a new motion whose coherence depends non-monotonically (resonantly) on the noise intensity.

A Simple Guide for Plotting a Proper Bifurcation Diagram

2021 ◽  
Vol 31 (01) ◽  
pp. 2150011
Author(s):  
Ali Jafari ◽  
Iqtadar Hussain ◽  
Fahimeh Nazarimehr ◽  
Seyed Mohammad Reza Hashemi Golpayegani ◽  
Sajad Jafari
Keyword(s):  
Bifurcation Diagram ◽  
Chaotic Systems ◽  
Critical Slowing Down ◽  
Initial Condition ◽  
Bifurcation Diagrams ◽  
Transient Time ◽  
Slowing Down ◽  
Critical Issues

In this paper, we propose a guideline for plotting the bifurcation diagrams of chaotic systems. We discuss numerical and mathematical facts in order to obtain more accurate and more elegant bifurcation diagrams. The importance of transient time and the phenomena of critical slowing down are investigated. Some critical issues related to multistability are discussed. Finally, a solution for fast obtaining an accurate sketch of the bifurcation diagram is presented. The solution is based on running the system for only one sample in each parameter value and using the system’s state in the previous value of the parameter as the initial condition.

Sign in / Sign up

Export Citation Format

Share Document