Synchronization, anti-synchronization and circuit realization of a novel hyper-chaotic system

Abstract

Purpose This paper aims to introduce a novel four-dimensional hyper-chaotic system with different hyper-chaotic attractors as certain parameters vary. The typical dynamical behaviors of the new hyper-chaotic system are discussed in detail. The control problem of these hyper-chaotic attractors is also investigated analytically and numerically. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components. Design/methodology/approach The adaptive control method is derived to achieve chaotic synchronization and anti-synchronization of the novel hyper-chaotic system with unknown parameters by making the synchronization and anti-synchronization error systems asymptotically stable at the origin based on Lyapunov stability theory. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components. Multisim simulations and electronic circuit experiments are consistent with MATLAB simulation results and they verify the existence of these hyper-chaotic attractors. Findings Comparisons among MATLAB simulations, Multisim simulation results and physical experimental results show that they are consistent with each other and demonstrate that changing attractors of the hyper-chaotic system exist. Originality/value The goal of this paper is to construct a new four-dimensional hyper-chaotic system with different attractors as certain parameters vary. The adaptive synchronization and anti-synchronization laws of the novel hyper-chaotic system are established based on Lyapunov stability theory. The corresponding electronic circuits for the novel hyper-chaotic system with different attractors are also implemented to illustrate the accuracy and efficiency of chaotic circuit design.

Robust adaptive anti-synchronization control of multiple uncertain chaotic systems of different orders

“…[23] accomplishes the ASC of two dynamical networks with both equivalent and different topological structures. Using the adaptive feedback control strategy, [24] studies the dynamics, control, synchronization, and AS of a novel hyperchaotic system with circuit realization. The paper [25] investigates the chaos synchronization and AS of two identical fractional-order chaotic systems using the active control technique.…”

“…[26] studies the synchronization and AS of two indistinguishable chaotic complex nonlinear frameworks. The works in [18][19][20][21][22][23][24][25][26][27] investigate the one-to-one system AS. The results in [28] are an improvement of the oneto-one system AS scheme to the CCAS of five chaotic systems with known parameters.…”

“…The reported ASC approaches [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] (among others) confine to the specific assumption that the required error information between the coupled hyper(chaotic) systems is known. These ASC techniques use the FL concept to develop feedback controllers for the AS.…”

“…The effect of these disturbances may shatter the ASC stability. The ASC approaches [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] either do not consider the effects of unknown SD and TD disturbances in the closed-loop or bounds of these disturbances are known in prior, which is hard to be determined in practice M(iii) The ASC scheme [20] (among others), use the signum 10650 function to tackle the effects of unknown SD and TD disturbances and to achieve the fast AS behaviour. The robust ASC approach [20] synthesis a large control effort that results in smaller tracking error and shorter transient response time.…”

“…The AS of UC systems offers theoretical complications in designing the feedback controllers. Such ASC schemes [28][29][30][31] produce large oscillations in the closedloop, which further become prominent in uncertain systems [32] M(v) The rates of convergence in the AS schemes [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] are slow, which affects the performance of such ASC methods in practical applications, for example, cellular radio systems, multi-agent systems, and wireless networks, etc…”