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.

scholarly journals A New Hamiltonian Chaotic System with Coexisting Chaotic Orbits and its Dynamical Analysis

2018 ◽  
Vol 7 (4) ◽  
pp. 2430
Author(s):  
Sundarapandian Vaidyanathan ◽  
Aceng Sambas ◽  
Sen Zhang ◽  
Mohamad Afendee Mohamed ◽  
Mustafa Mamat
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Research Work ◽  
Classical Mechanics ◽  
Dynamical Analysis ◽  
Galactic Centre ◽  
Chaotic Orbits ◽  
Nonlinear Motion ◽  
Dynamical Properties

Hamiltonian chaotic systems are conservative chaotic systems which arise in many applications in Classical Mechanics. A famous Hamiltonian chaotic system is the H´enon-Heiles system (1964), which was modeled by H´enon and Heiles, describing the nonlinear motion of a star around a galactic centre with the motion restricted to a plane. In this research work, by modifying the dynamics of the H´enon-Heiles system (1964), we obtain a new Hamiltonian chaotic system with coexisting chaotic orbits. We describe the dynamical properties of the new Hamiltonian chaotic system.

Seismic Response Analysis on a Chaotic System

2013 ◽  
Vol 639-640 ◽  
pp. 911-916
Author(s):  
Cui Xiang Liang
Keyword(s):  
Seismic Response ◽  
Chaotic System ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Response Analysis ◽  
Bifurcation Diagrams ◽  
Seismic Response Analysis ◽  
Nonlinear Seismic Response ◽  
Hyperbolic Equilibrium ◽  
Hyperbolic Equilibrium Point

This paper is concerned with the dynamical behavior of a chaotic system which is a model for seismic response of structures. The local bifurcation of the non-hyperbolic equilibrium point of the chaotic system is investigated by using center manifold method. The transcritical bifurcation is analyzed in detail. Based on numerical simulations, spectrums of maximal Lyapunov exponent and the bifurcation diagrams are presented for the dynamic analysis. The method proposed can be used as a reference of nonlinear seismic response analysis.

scholarly journals A Novel Chaotic System without Equilibrium: Dynamics, Synchronization, and Circuit Realization

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ahmad Taher Azar ◽  
Christos Volos ◽  
Nikolaos A. Gerodimos ◽  
George S. Tombras ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Unstable Equilibrium ◽  
Physical Realization ◽  
Circuit Realization ◽  
Equilibrium Dynamics ◽  
Dynamical Properties ◽  
Shilnikov Criterion ◽  
New System

A few special chaotic systems without unstable equilibrium points have been investigated recently. It is worth noting that these special systems are different from normal chaotic ones because the classical Shilnikov criterion cannot be used to prove chaos of such systems. A novel unusual chaotic system without equilibrium is proposed in this work. We discover dynamical properties as well as the synchronization of the new system. Furthermore, a physical realization of the system without equilibrium is also implemented to illustrate its feasibility.

Dynamical analysis and triple compound combination anti-synchronization of novel fractional chaotic system

2021 ◽  
pp. 107754632098773
Author(s):  
Pushali Trikha ◽  
Lone S Jahanzaib ◽  
Nasreen ◽  
Dumitru Baleanu
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Dynamical Analysis ◽  
Phase Portraits ◽  
Adaptive Sliding Mode Control ◽  
The Novel ◽  
Novel Technique ◽  
Analysis Phase ◽  
Fractional Chaotic System

This study introduces a novel 3-D fractional chaotic system with two quadratic terms and no equilibrium point. Thorough dynamical analysis of the introduced system is done studying Lyapunov dynamics with respect to fractional order and parameter value, Kaplan–Yorke dimension, bifurcation analysis, phase portraits, existence, and uniqueness of solution, dissipative and symmetric character, etc. The novel system is anti-synchronized using the novel technique ‘triple compound combination’ considering uncertainties and disturbances on a parallel system by two methods—nonlinear and adaptive sliding mode control. A proposed application of achieved synchronization in secure communication is presented. A comparative study of obtained results with published literature is also presented.

Synchronisation and Circuit Realisation of Chaotic Hartley System

2018 ◽  
Vol 73 (6) ◽  
pp. 521-531 ◽  
Author(s):  
Metin Varan ◽  
Akif Akgül ◽  
Emre Güleryüz ◽  
Kasım Serbest
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Circuit Model ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Model Simulations ◽  
Modelling Problem ◽  
Complex Chaotic System

AbstractHartley chaotic system is topologically the simplest, but its dynamical behaviours are very rich and its synchronisation has not been seen in literature. This paper aims to introduce a simple chaotic system which can be used as alternative to classical chaotic systems in synchronisation fields. Time series, phase portraits, and bifurcation diagrams reveal the dynamics of the mentioned system. Chaotic Hartley model is also supported with electronic circuit model simulations. Its exponential dynamics are hard to realise on circuit model; this paper is the first in literature that handles such a complex modelling problem. Modelling, synchronisation, and circuit realisation of the Hartley system are implemented respectively in MATLAB-Simulink and ORCAD environments. The effectiveness of the applied synchronisation method is revealed via numerical methods, and the results are discussed. Retrieved results show that this complex chaotic system can be used in secure communication fields.

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.

LAG PROJECTIVE STOCHASTIC PERTURBED SYNCHRONIZATION FOR CHAOTIC SYSTEMS AND ITS APPLICATION IN SECURE COMMUNICATION

2008 ◽  
Vol 22 (24) ◽  
pp. 4175-4188 ◽  
Author(s):  
YANG TANG ◽  
JIAN-AN FANG ◽  
LIANG CHEN
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Stochastic Perturbation ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Adaptive Feedback ◽  
Communication Scheme ◽  
Simulation Results ◽  
Feedback Method

In this paper, a simple and systematic adaptive feedback method for achieving lag projective stochastic perturbed synchronization of a new four-wing chaotic system with unknown parameters is presented. Moreover, a secure communication scheme based on the adaptive feedback lag projective synchronization of the new chaotic systems with stochastic perturbation and unknown parameters is presented. The simulation results show the feasibility of the proposed method.

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.

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