scholarly journals Basin of Attraction Analysis of New Memristor-Based Fractional-Order Chaotic System

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Long Ding ◽  
Li Cui ◽  
Fei Yu ◽  
Jie Jin
Keyword(s):  
Phase Space ◽  
Lyapunov Exponent ◽  
Fractional Order ◽  
Chaotic System ◽  
Exponential Function ◽  
Local Minimum ◽  
System Analysis ◽  
Basin Of Attraction ◽  
Stable Point ◽  
The Basin Of Attraction

Memristor is the fourth basic electronic element discovered in addition to resistor, capacitor, and inductor. It is a nonlinear gadget with memory features which can be used for realizing chaotic, memory, neural network, and other similar circuits and systems. In this paper, a novel memristor-based fractional-order chaotic system is presented, and this chaotic system is taken as an example to analyze its dynamic characteristics. First, we used Adomian algorithm to solve the proposed fractional-order chaotic system and yield a chaotic phase diagram. Then, we examined the Lyapunov exponent spectrum, bifurcation, SE complexity, and basin of attraction of this system. We used the resulting Lyapunov exponent to describe the state of the basin of attraction of this fractional-order chaotic system. As the local minimum point of Lyapunov exponential function is the stable point in phase space, when this stable point in phase space comes into the lowest region of the basin of attraction, the solution of the chaotic system is yielded. In the analysis, we yielded the solution of the system equation with the same method used to solve the local minimum of Lyapunov exponential function. Our system analysis also revealed the multistability of this system.

Some New Dissipative Chaotic Systems with Cyclic Symmetry

2018 ◽  
Vol 28 (13) ◽  
pp. 1850164 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Shirin Panahi ◽  
Anitha Karthikeyan ◽  
Ahmed Alsaedi ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Basin Of Attraction ◽  
Cyclic Symmetry ◽  
Circuit Implementation ◽  
New Chaotic System ◽  
The Basin Of Attraction

Designing new chaotic system with specific features is an interesting field in nonlinear dynamics. In this paper, some new chaotic systems with cyclic symmetry are proposed. In order to understand the overall behavior of such systems, the dynamical analyses such as stability analysis, bifurcation and Lyapunov exponent analysis are done. The accurate examination of bifurcation plot represents that these systems are multistable which makes them more interesting. Also, the basin of attraction of these systems is investigated to detect the type of attractors of these systems which are self-excited. Finally, the circuit implementation is carried out to show their feasibility.

scholarly journals A Fractional-Order Chaotic System with an Infinite Number of Equilibrium Points

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ping Zhou ◽  
Kun Huang ◽  
Chun-de Yang
Keyword(s):  
Lyapunov Exponent ◽  
Fractional Order ◽  
Chaotic System ◽  
Infinite Number ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Chaotic Synchronization ◽  
Order System ◽  
Largest Lyapunov Exponent ◽  
Synchronization Scheme

A new 4D fractional-order chaotic system, which has an infinite number of equilibrium points, is introduced. There is no-chaotic behavior for its corresponded integer-order system. We obtain that the largest Lyapunov exponent of this 4D fractional-order chaotic system is 0.8939 and yield the chaotic attractor. A chaotic synchronization scheme is presented for this 4D fractional-order chaotic system. Numerical simulations is verified the effectiveness of the proposed scheme.

Infinite Multistability in a Self-Reproducing Chaotic System

2017 ◽  
Vol 27 (10) ◽  
pp. 1750160 ◽  
Author(s):  
Chunbiao Li ◽  
Julien Clinton Sprott ◽  
Wen Hu ◽  
Yujie Xu
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Chaotic System ◽  
Basin Of Attraction ◽  
Initial Condition ◽  
Coexisting Attractors ◽  
Coordinate Axis

Multistability exists in various regimes of dynamical systems and in different combinations, among which there is a special one generated by self-reproduction. In this paper, we describe a method for constructing self-reproducing systems from a unique class of variable-boostable systems whose coexisting attractors reside in the phase space along a specific coordinate axis and any of which can be selected by choosing an initial condition in its corresponding basin of attraction.

scholarly journals Strategies for an Efficient Official Publicity Campaign

2021 ◽  
Vol 183 (2) ◽  
Author(s):  
Juan Neirotti
Keyword(s):  
Fixed Point ◽  
Public Opinion ◽  
Phase Space ◽  
Fixed Points ◽  
Basin Of Attraction ◽  
Opinion Formation ◽  
Publicity Campaign ◽  
The Basin Of Attraction

AbstractWe consider the process of opinion formation, in a society where there is a set of rules B that indicates whether a social instance is acceptable. Public opinion is formed by the integration of the voters’ attitudes which can be either conservative (mostly in agreement with B) or liberal (mostly in disagreement with B and in agreement with peer voters). These attitudes are represented by stable fixed points in the phase space of the system. In this article we study the properties of a perturbative term, mimicking the effects of a publicity campaign, that pushes the system from the basin of attraction of the liberal fixed point into the basin of the conservative point, when both fixed points are equally likely.

A COMPUTER-ASSISTED STUDY OF GLOBAL DYNAMIC TRANSITIONS FOR A NONINVERTIBLE SYSTEM

2007 ◽  
Vol 17 (04) ◽  
pp. 1305-1321 ◽  
Author(s):  
RAYMOND A. ADOMAITIS ◽  
IOANNIS G. KEVREKIDIS ◽  
RAFAEL DE LA LLAVE
Keyword(s):  
Phase Space ◽  
Basin Of Attraction ◽  
Basins Of Attraction ◽  
Computer Assisted ◽  
Discrete Time System ◽  
Time System ◽  
Invariant Circle ◽  
Global Dynamic ◽  
Assisted Analysis ◽  
The Basin Of Attraction

We present a computer-assisted analysis of the phase space features and bifurcations of a noninvertible, discrete-time system. Our focus is on the role played by noninvertibility in generating disconnected basins of attraction and the breakup of invariant circle solutions. Transitions between basin of attraction structures are identified and organized according to "levels of complexity," a term we define in this paper. In particular, we present an algorithm that provides a computational approximation to the boundary (in phase space) separating points with different preimage behavior. The interplay between this boundary and other phase space features is shown to be crucial in understanding global bifurcations and transitions in the structure of the basin of attraction.

scholarly journals On embedding of invariant manifolds of the simplest Morse-Smale flows with heteroclinical intersections

2018 ◽  
Vol 20 (4) ◽  
pp. 378-383
Author(s):  
E. Ya. Gurevich ◽  
D. A. Pavlova
Keyword(s):  
Phase Space ◽  
Invariant Manifolds ◽  
Basin Of Attraction ◽  
Classification Problem ◽  
Closed Curve ◽  
Topological Classification ◽  
Dimensional Phase Space ◽  
Smale Flows ◽  
Source Sink ◽  
The Basin Of Attraction

We study a structure of four-dimensional phase space decomposition on trajectories of Morse-Smale flows admitting heteroclinical intersections. More precisely, we consider a class G(S4) of Morse-Smale flows on the sphere S4 such that for any flow f∈G(S4) its non-wandering set consists of exactly four equilibria: source, sink and two saddles. Wandering set of such flows contains finite number of heteroclinical curves that belong to intersection of invariant manifolds of saddle equilibria. We describe a topology of embedding of saddle equilibria’s invariant manifolds; that is the first step in the solution of topological classification problem. In particular, we prove that the closures of invariant manifolds of saddle equlibria that do not contain heteroclinical curves are locally flat 2-sphere and closed curve. These manifolds are attractor and repeller of the flow. In set of orbits that belong to the basin of attraction or repulsion we construct a section that is homeomoprhic to the direct product S2×S1. We study a topology of intersection of saddle equlibria’s invariant manifolds with this section.

scholarly journals New Fractional Order Chaotic System: Analysis, Synchronization, and it’s Application

2021 ◽  
Vol 17 (1) ◽  
pp. 1-9
Author(s):  
Zain_Aldeen Rahman ◽  
Basil Jassim ◽  
Yasir Al_Yasir
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
System Analysis ◽  
Three Dimensional ◽  
Nonlinear Dynamic System ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Communication Scheme ◽  
New System

In this paper, a new nonlinear dynamic system, new three-dimensional fractional order complex chaotic system, is presented. This new system can display hidden chaotic attractors or self-excited chaotic attractors. The Dynamic behaviors of this system have been considered analytically and numerically. Different means including the equilibria, chaotic attractor phase portraits, the Lyapunov exponent, and the bifurcation diagrams are investigated to show the chaos behavior in this new system. Also, a synchronization technique between two identical new systems has been developed in master- slave configuration. The two identical systems are synchronized quickly. Furthermore, the master-slave synchronization is applied in secure communication scheme based on chaotic masking technique. In the application, it is noted that the message is encrypted and transmitted with high security in the transmitter side, in the other hand the original message has been discovered with high accuracy in the receiver side. The corresponding numerical simulation results proved the efficacy and practicability of the developed synchronization technique and its application

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