Different Families of Hidden Attractors in a New Chaotic System with Variable Equilibrium

2017 ◽  
Vol 27 (09) ◽  
pp. 1750138 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Sajad Jafari ◽  
Christos Volos ◽  
Tomasz Kapitaniak
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
View Point ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
Complex Dynamical Behavior ◽  
New System

A new chaotic system having variable equilibrium is introduced in this paper. The presence of an infinite number of equilibrium points, a stable equilibrium, and no-equilibrium is observed in the system. Interestingly, this system is classified as a rare system with hidden attractors from the view point of computation. Complex dynamical behavior and a circuital implementation of the new system have been investigated in our work.

Constructing a Chaotic System with an Infinite Number of Equilibrium Points

2016 ◽  
Vol 26 (13) ◽  
pp. 1650225 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Sajad Jafari ◽  
Tomasz Kapitaniak
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Chaotic Systems ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Hidden Attractors ◽  
Memristive Device ◽  
New System

The chaotic systems with hidden attractors, such as chaotic systems with a stable equilibrium, chaotic systems with infinite equilibria or chaotic systems with no equilibrium have been investigated recently. However, the relationships between them still need to be discovered. This work explains how to transform a system with one stable equilibrium into a new system with an infinite number of equilibrium points by using a memristive device. Furthermore, some other new systems with infinite equilibria are also constructed to illustrate the introduced methodology.

scholarly journals A New Chaotic System with Only Nonhyperbolic Equilibrium Points: Dynamics and Its Engineering Application

Complexity ◽  
2022 ◽  
Vol 2022 ◽  
pp. 1-16
Author(s):  
Maryam Zolfaghari-Nejad ◽  
Mostafa Charmi ◽  
Hossein Hassanpoor
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Equilibrium Points ◽  
Engineering Application ◽  
Period Doubling ◽  
Spectral Entropy ◽  
Multiple Attractors ◽  
Initial Values ◽  
New Chaotic System ◽  
New System

In this work, we introduce a new non-Shilnikov chaotic system with an infinite number of nonhyperbolic equilibrium points. The proposed system does not have any linear term, and it is worth noting that the new system has one equilibrium point with triple zero eigenvalues at the origin. Also, the novel system has an infinite number of equilibrium points with double zero eigenvalues that are located on the z -axis. Numerical analysis of the system reveals many strong dynamics. The new system exhibits multistability and antimonotonicity. Multistability implies the coexistence of many periodic, limit cycle, and chaotic attractors under different initial values. Also, bifurcation analysis of the system shows interesting phenomena such as periodic window, period-doubling route to chaos, and inverse period-doubling bifurcations. Moreover, the complexity of the system is analyzed by computing spectral entropy. The spectral entropy distribution under different initial values is very scattered and shows that the new system has numerous multiple attractors. Finally, chaos-based encoding/decoding algorithms for secure data transmission are developed by designing a state chain diagram, which indicates the applicability of the new chaotic system.

scholarly journals A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sundarapandian Vaidyanathan ◽  
Xiong Wang
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Equilibrium Analysis ◽  
Chaotic Attractors ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
Topological Horseshoes

Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control.

A Novel No-Equilibrium Chaotic System with Multiwing Butterfly Attractors

2015 ◽  
Vol 25 (04) ◽  
pp. 1550056 ◽  
Author(s):  
Fadhil Rahma Tahir ◽  
Sajad Jafari ◽  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Xiong Wang
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
State Feedback ◽  
Equilibrium Points ◽  
Research Topic ◽  
Feedback Controller ◽  
Strange Attractors ◽  
State Feedback Controller ◽  
New Chaotic System ◽  
New System

Discovering unknown features of no-equilibrium systems with hidden strange attractors is an attractive research topic. This paper presents a novel no-equilibrium chaotic system that is constructed by using a state feedback controller. Interestingly, the new system can exhibit multiwing butterfly attractors. Moreover, a new chaotic system with an infinite number of equilibrium points, which can generate multiscroll attractors, is also proposed by applying the introduced methodology.

Jacobi analysis for an unusual 3D autonomous system

2020 ◽  
Vol 17 (04) ◽  
pp. 2050062 ◽  
Author(s):  
Chunsheng Feng ◽  
Qiujian Huang ◽  
Yongjian Liu
Keyword(s):  
Chaotic System ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Chen System ◽  
Parameter Region ◽  
Stable Equilibria ◽  
The Lorenz System ◽  
Deviation Vector

Little seems to be known about the study of the chaotic system with only Lyapunov stable equilibria from the perspective of differential geometry. Therefore, this paper presents Jacobi analysis of an unusual three-dimensional (3D) autonomous chaotic system. Under certain parameter conditions, this system has positive Lyapunov exponents and only two linear stable equilibrium points, which means that chaotic attractor and Lyapunov stable equilibria coexist. The dynamical behavior of the deviation vector near the whole trajectories (including all equilibrium points) is analyzed in detail. The results show that the value of the deviation curvature tensor at equilibrium points is only related to parameters; the two equilibrium points of the system are Jacobi stable if the parameters satisfy certain conditions. Particularly, for a specific set of parameters, the linear stable equilibrium points of the system are always Jacobi unstable. A periodic orbit that is Lyapunov stable is also proven to be always Jacobi unstable. Next, Jacobi-stable regions of the Lorenz system, the Chen system and the system under study are compared for specific parameters. It can be found that although these three chaotic systems are very similar, their regions of Jacobi stable parameters are much different. Finally, by comparing Jacobi stability with Lyapunov stability, the obtained results demonstrate that the Jacobi stable parameter region is basically symmetric with the Lyapunov stable parameter region.

scholarly journals A New Four-Scroll Chaotic System with a Self-Excited Attractor and Circuit Implementation

2018 ◽  
Vol 7 (3) ◽  
pp. 1931 ◽  
Author(s):  
Sivaperumal Sampath ◽  
Sundarapandian Vaidyanathan ◽  
Aceng Sambas ◽  
Mohamad Afendee ◽  
Mustafa Mamat ◽  
...  
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Electronic Circuit Simulation ◽  
New System

This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The proposed system is a new addition to existing multi-scroll chaotic systems in the literature. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. As the new four-scroll chaotic system is shown to have three unstable equilibrium points, it has a self-excited chaotic attractor. An electronic circuit simulation of the new four-scroll chaotic system is shown using MultiSIM to check the feasibility of the four-scroll chaotic model.

From Wang–Chen System with Only One Stable Equilibrium to a New Chaotic System Without Equilibrium

2017 ◽  
Vol 27 (06) ◽  
pp. 1750097 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Xiong Wang ◽  
Sajad Jafari ◽  
Christos Volos ◽  
Tomasz Kapitaniak
Keyword(s):  
Chaotic System ◽  
State Feedback ◽  
Stable Equilibrium ◽  
Hidden Attractors ◽  
Chen System ◽  
State Variable ◽  
New Chaotic System

Wang–Chen system with only one stable equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang–Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one stable equilibrium to hidden attractors without equilibrium.

scholarly journals A New Chaotic System with a Pear-shaped Equilibrium and its Circuit Simulation

2018 ◽  
Vol 8 (6) ◽  
pp. 4951 ◽  
Author(s):  
Aceng Sambas ◽  
Sundarapandian Vaidyanathan ◽  
Mustafa Mamat ◽  
Muhammad Afendee Mohamed ◽  
Mada Sanjaya WS
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Equilibrium Curve ◽  
New Chaotic System ◽  
Electronic Circuit Simulation ◽  
New System

This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and makes a valuable addition to existing chaotic systems with infinite equilibrium points in the literature. The new chaotic system has a total of five nonlinearities. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system are unveiled. An electronic circuit simulation of the new chaotic system with pear-shaped equilibrium curve is shown using Multisim to check the model feasibility.

A Chaotic System with Different Families of Hidden Attractors

2016 ◽  
Vol 26 (08) ◽  
pp. 1650139 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Sundarapandian Vaidyanathan ◽  
Tomasz Kapitaniak ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Infinite Number ◽  
Mathematical Analysis ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Dynamical Behaviors

The presence of hidden attractors in dynamical systems has received considerable attention recently both in theory and applications. A novel three-dimensional autonomous chaotic system with hidden attractors is introduced in this paper. It is exciting that this chaotic system can exhibit two different families of hidden attractors: hidden attractors with an infinite number of equilibrium points and hidden attractors without equilibrium. Dynamical behaviors of such system are discovered through mathematical analysis, numerical simulations and circuit implementation.

scholarly journals Dynamical Analysis and Simulation of a New Lorenz-Like Chaotic System

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
You Li ◽  
Ming Zhao ◽  
Fengjie Geng
Keyword(s):  
Chaotic System ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Heteroclinic Orbits ◽  
Dynamical Analysis ◽  
Poincaré Compactification ◽  
Stable And Unstable Manifolds ◽  
Dynamical Behaviors ◽  
New Chaotic System ◽  
New Type

This work presents and investigates a new chaotic system with eight terms. By numerical simulation, the two-scroll chaotic attractor is found for some certain parameters. And, by theoretical analysis, we discuss the dynamical behavior of the new-type Lorenz-like chaotic system. Firstly, the local dynamical properties, such as the distribution and the local stability of all equilibrium points, the local stable and unstable manifolds, and the Hopf bifurcations, are all revealed as the parameters varying in the space of parameters. Secondly, by applying the way of Poincaré compactification in ℝ 3 , the dynamics at infinity are clearly analyzed. Thirdly, combining the dynamics at finity and those at infinity, the global dynamical behaviors are formulated. Especially, we have proved the existence of the infinite heteroclinic orbits. Furthermore, all obtained theoretical results in this paper are further verified by numerical simulations.

Sign in / Sign up

Export Citation Format

Share Document