Dynamics, circuit realization, control and synchronization of a hyperchaotic hyperjerk system with coexisting attractors

2017 ◽  
Vol 89 (3) ◽  
pp. 1673-1687 ◽  
Author(s):  
Xiong Wang ◽  
Sundarapandian Vaidyanathan ◽  
Christos Volos ◽  
Viet-Thanh Pham ◽  
Tomasz Kapitaniak
Keyword(s):  
Coexisting Attractors ◽  
Circuit Realization ◽  
Control And Synchronization ◽  
Hyperjerk System

A new 4-D chaotic hyperjerk system with coexisting attractors, its active backstepping control, and circuit realization

2021 ◽  
pp. 73-94
Author(s):  
Aceng Sambas ◽  
Sundarapandian Vaidyanathan ◽  
Sen Zhang ◽  
Mohamad Afendee Mohamed ◽  
Yicheng Zeng ◽  
...  
Keyword(s):  
Backstepping Control ◽  
Coexisting Attractors ◽  
Circuit Realization ◽  
Hyperjerk System

Multistability and Coexisting Attractors in a New Circulant Chaotic System

2019 ◽  
Vol 29 (13) ◽  
pp. 1950174 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
Fawaz E. Alsaadi ◽  
Fahimeh Nazarimehr ◽  
...  
Keyword(s):  
Fractional Order ◽  
Order System ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Coexisting Attractors ◽  
Circuit Realization ◽  
Chaotic Flow ◽  
Fractional Order Model ◽  
Dynamical Properties ◽  
Fractional Orders

In this paper, a new four-dimensional chaotic flow is proposed. The system has a cyclic symmetry in its structure and shows a complicated, chaotic attractor. The dynamical properties of the system are investigated. The system shows multistability in an interval of its parameter. Fractional order model of the proposed system is discussed in various fractional orders. Bifurcation analysis of the fractional order system shows that it has a kind of multistability like the integer order system, which is a very rare phenomenon. Circuit realization of the proposed system is also carried out to show that it is usable for engineering applications.

scholarly journals A Memristive Hyperjerk Chaotic System: Amplitude Control, FPGA Design, and Prediction with Artificial Neural Network

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Ran Wang ◽  
Chunbiao Li ◽  
Serdar Çiçek ◽  
Karthikeyan Rajagopal ◽  
Xin Zhang
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fpga Design ◽  
Initial Value ◽  
Circuit Realization ◽  
Amplitude Control ◽  
Extreme Multistability ◽  
Artificial Neural ◽  
Hyperjerk System ◽  
Line Of Equilibria

An amplitude controllable hyperjerk system is constructed for chaos producing by introducing a nonlinear factor of memristor. In this case, the amplitude control is realized from a single coefficient in the memristor. The hyperjerk system has a line of equilibria and also shows extreme multistability indicated by the initial value-associated bifurcation diagram. FPGA-based circuit realization is also given for physical verification. Finally, the proposed memristive hyperjerk system is successfully predicted with artificial neural networks for AI based engineering applications.

scholarly journals Analysis, Synchronization, and Robotic Application of a Modified Hyperjerk Chaotic System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Lazaros Moysis ◽  
Eleftherios Petavratzis ◽  
Muhammad Marwan ◽  
Christos Volos ◽  
Hector Nistazakis ◽  
...  
Keyword(s):  
Chaos Theory ◽  
Nonlinear Term ◽  
Dynamical Analysis ◽  
Coexisting Attractors ◽  
Hyperbolic Sine ◽  
Route To Chaos ◽  
Hyperjerk System ◽  
Parameter Values ◽  
Robotic Application ◽  
Hyperbolic Sine Function

In this work, a novel hyperjerk system, with hyperbolic sine function as the only nonlinear term, is proposed, as a modification of a hyperjerk system proposed by Leutcho et al. First, a dynamical analysis on the system is performed and interesting phenomena concerning chaos theory, such as route to chaos, antimonotonicity, crisis, and coexisting attractors, are studied. For this reason, the system’s bifurcation diagrams with respect to different parameter values are plotted and its Lyapunov exponents are computed. Afterwards, the synchronization of the system is considered, using active control. The proposed system is then applied, as a chaotic generator, to the problem of chaotic path planning, using a combination of sampling and a modulo tactic technique.

scholarly journals Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation

2015 ◽  
Vol 25 (1) ◽  
pp. 135-158 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos ◽  
Viet-Thanh Pham ◽  
Kavitha Madhavan
Keyword(s):  
Chaotic System ◽  
Research Work ◽  
The Novel ◽  
Adaptive Backstepping ◽  
Qualitative Properties ◽  
Unknown Parameters ◽  
Circuit Realization ◽  
Backstepping Controller ◽  
Hyperjerk System ◽  
Adaptive Backstepping Controller

Abstract A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n ⩾ 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n ⩾ 4. In this research work, a 4-D novel hyperchaotic hyperjerk system has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel hyperjerk system are obtained as L1 = 0.1448, L2 = 0.0328, L3 = 0 and L4 = −1.1294. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as DKY= 3.1573. Next, an adaptive backstepping controller is designed to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global hyperchaos synchronization of the identical novel hyperjerk systems with three unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using SPICE is presented in detail to confirm the feasibility of the theoretical hyperjerk model.

scholarly journals Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method

2016 ◽  
Vol 26 (3) ◽  
pp. 311-338 ◽  
Author(s):  
Sundarapandian Vaidyanathan
Keyword(s):  
Control Method ◽  
Research Work ◽  
Adaptive Controller ◽  
Backstepping Control ◽  
The Novel ◽  
Qualitative Properties ◽  
Unknown Parameters ◽  
A Chain ◽  
Control And Synchronization ◽  
Hyperjerk System

AbstractA hyperjerk system is a dynamical system, which is modelled by annth order ordinary differential equation withn≥ 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system ofnfirst order ordinary differential equations withn≥ 4. In this research work, a 4-D novel hyperchaotic hyperjerk system with two nonlinearities has been proposed, and its qualitative properties have been detailed. The novel hyperjerk system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel hyperjerk system are obtained asL1= 0.14219,L2= 0.04605,L3= 0 andL4= −1.39267. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained asDKY= 3.1348. Next, an adaptive controller is designed via backstepping control method to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive controller is designed via backstepping control method to achieve global synchronization of the identical novel hyperjerk systems with three unknown parameters. MATLAB simulations are shown to illustrate all the main results derived in this research work on a novel hyperjerk system.

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