A chaotic system with a single unstable node

2015 ◽  
Vol 379 (36) ◽  
pp. 2030-2036 ◽  
Author(s):  
J.C. Sprott ◽  
Sajad Jafari ◽  
Viet-Thanh Pham ◽  
Zahra Sadat Hosseini
Keyword(s):  
Chaotic System ◽  
Unstable Node

scholarly journals Dynamical Analysis and Periodic Solution of a Chaotic System with Coexisting Attractors

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Mingshu Chen ◽  
Zhen Wang ◽  
Xiaojuan Zhang ◽  
Huaigu Tian
Keyword(s):  
Chaotic System ◽  
Vector Fields ◽  
Dynamical Analysis ◽  
Stable Node ◽  
Polynomial Vector Fields ◽  
Coexisting Attractors ◽  
Poincaré Compactification ◽  
Unstable Node ◽  
New Chaotic System ◽  
Multiple Coexisting Attractors

Chaotic attractors with no equilibria, with an unstable node, and with stable node-focus are presented in this paper. The conservative solutions are investigated by the semianalytical and seminumerical method. Furthermore, multiple coexisting attractors are investigated, and circuit is carried out. To study the system’s global structure, dynamics at infinity for this new chaotic system are studied using Poincaré compactification of polynomial vector fields in R 3 . Meanwhile, the dynamics near the infinity of the singularities are obtained by reducing the system’s dimensions on a Poincaré ball. The averaging theory analyzes the periodic solution’s stability or instability that bifurcates from Hopf-zero bifurcation.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

scholarly journals Complex dynamical behaviors of a novel exponential hyper–chaotic system and its application in fast synchronization and color image encryption

2021 ◽  
Vol 104 (1) ◽  
pp. 003685042110033
Author(s):  
Javad Mostafaee ◽  
Saleh Mobayen ◽  
Behrouz Vaseghi ◽  
Mohammad Vahedi ◽  
Afef Fekih
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Sliding Mode ◽  
Color Image ◽  
Equilibrium Points ◽  
Lyapunov Stability Theory ◽  
System Stability ◽  
Color Image Encryption ◽  
Terminal Sliding Mode ◽  
Finite Time Stability

This paper proposes a novel exponential hyper–chaotic system with complex dynamic behaviors. It also analyzes the chaotic attractor, bifurcation diagram, equilibrium points, Poincare map, Kaplan–Yorke dimension, and Lyapunov exponent behaviors. A fast terminal sliding mode control scheme is then designed to ensure the fast synchronization and stability of the new exponential hyper–chaotic system. Stability analysis was performed using the Lyapunov stability theory. One of the main features of the proposed controller is the finite time stability of the terminal sliding surface designed with high–order power function of error and derivative of error. The approach was implemented for image cryptosystem. Color image encryption was carried out to confirm the performance of the new hyper–chaotic system. For image encryption, the DNA encryption-based RGB algorithm was used. Performance assessment of the proposed approach confirmed the ability of the proposed hyper–chaotic system to increase the security of image encryption.

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