A novel memristor-based multi-scroll hyperchaotic system is proposed.Based on a voltage-controlled memristor and a modulating sine nonlinear function,a novel method is proposed to generate the multi-scroll hyperchaoti...A novel memristor-based multi-scroll hyperchaotic system is proposed.Based on a voltage-controlled memristor and a modulating sine nonlinear function,a novel method is proposed to generate the multi-scroll hyperchaotic attractors.Firstly,a multi-scroll chaotic system is constructed from a three-dimensional chaotic system by designing a modulating sine nonlinear function.Then,a voltage-controlled memristor is introduced into the above-designed multi-scroll chaotic system.Thus,a memristor-based multi-scroll hyperchaotic system is generated,and this hyperchaotic system can produce various coexisting hyperchaotic attractors with different topological structures.Moreover,different number of scrolls and different topological attractors can be obtained by varying the initial conditions of this system without changing the system parameters.The Lyapunov exponents,bifurcation diagrams and basins of attraction are given to analyze the dynamical characteristics of the multi-scroll hyperchaotic system.Besides,the field programmable gate array(FPGA)based digital implementation of the memristor-based multi-scroll hyperchaotic system is carried out.The experimental results of the FPGA-based digital circuit are displayed on the oscilloscope.展开更多
The aim of this paper is to introduce and investigate chaotic and hyperchaotic complex jerk equations. The jerk equations describe various phenomena in engineering and physics, for example, electrical circuits, laser ...The aim of this paper is to introduce and investigate chaotic and hyperchaotic complex jerk equations. The jerk equations describe various phenomena in engineering and physics, for example, electrical circuits, laser physics, mechanical oscillators, damped harmonic oscillators, and biological systems. Properties of these systems are studied and their Lyapunov exponents are calculated. The dynamics of these systems is rich in wide range of systems parameters. The control of chaotic attractors of the complex jerk equation is investigated. The Lyapunov exponents are calculated to show that the chaotic behavior is converted to regular behavior.展开更多
A novel 6D dissipative model with an unstable equilibrium point is introduced herein.Some of the dynamic characteristics of the proposed model were explored via analyses and numerical simulations including critical po...A novel 6D dissipative model with an unstable equilibrium point is introduced herein.Some of the dynamic characteristics of the proposed model were explored via analyses and numerical simulations including critical points,stability,Lyapunov exponents,time phase portraits,and circuit implementation.Also,anti-synchronization phenomena were implemented on the new system.Firstly,the error dynamics is found.Then,four different controllers are adopted to stabilize this error relying on the nonlinear control technique with two main ways:linearization and Lyapunov stability theory.In comparison with previous works,the present controllers realize anti-synchronization based on another method/linearization method.Finally,a comparison between the two ways was made.The simulation results show the effectiveness and accuracy of the first analytical strategy.展开更多
基金the National Natural Sciene Foundation of China(Grant Nos.61973199 and 61973200)the Taishan Scholar Project of Shandong Province of China。
文摘A novel memristor-based multi-scroll hyperchaotic system is proposed.Based on a voltage-controlled memristor and a modulating sine nonlinear function,a novel method is proposed to generate the multi-scroll hyperchaotic attractors.Firstly,a multi-scroll chaotic system is constructed from a three-dimensional chaotic system by designing a modulating sine nonlinear function.Then,a voltage-controlled memristor is introduced into the above-designed multi-scroll chaotic system.Thus,a memristor-based multi-scroll hyperchaotic system is generated,and this hyperchaotic system can produce various coexisting hyperchaotic attractors with different topological structures.Moreover,different number of scrolls and different topological attractors can be obtained by varying the initial conditions of this system without changing the system parameters.The Lyapunov exponents,bifurcation diagrams and basins of attraction are given to analyze the dynamical characteristics of the multi-scroll hyperchaotic system.Besides,the field programmable gate array(FPGA)based digital implementation of the memristor-based multi-scroll hyperchaotic system is carried out.The experimental results of the FPGA-based digital circuit are displayed on the oscilloscope.
文摘The aim of this paper is to introduce and investigate chaotic and hyperchaotic complex jerk equations. The jerk equations describe various phenomena in engineering and physics, for example, electrical circuits, laser physics, mechanical oscillators, damped harmonic oscillators, and biological systems. Properties of these systems are studied and their Lyapunov exponents are calculated. The dynamics of these systems is rich in wide range of systems parameters. The control of chaotic attractors of the complex jerk equation is investigated. The Lyapunov exponents are calculated to show that the chaotic behavior is converted to regular behavior.
文摘A novel 6D dissipative model with an unstable equilibrium point is introduced herein.Some of the dynamic characteristics of the proposed model were explored via analyses and numerical simulations including critical points,stability,Lyapunov exponents,time phase portraits,and circuit implementation.Also,anti-synchronization phenomena were implemented on the new system.Firstly,the error dynamics is found.Then,four different controllers are adopted to stabilize this error relying on the nonlinear control technique with two main ways:linearization and Lyapunov stability theory.In comparison with previous works,the present controllers realize anti-synchronization based on another method/linearization method.Finally,a comparison between the two ways was made.The simulation results show the effectiveness and accuracy of the first analytical strategy.
