Abstract
This article is investigating from one of best control technique known as periodically intermittent discrete observation control (PIDOC), the problem of global synchronization based on a relay configuration of three novel hyperchaotic oscillators of three-components (NHO) operating at high frequency. Contrary to traditional periodically intermittent control based on continuous-time state observations, PIDOC used here, chooses discrete-time state observations in work time during a control period. Our analysis has been limited to a range of parameters for which the NHO-type oscillator exhibits bursting oscillations. The global conditions of stability for non-adaptive and adaptive cases have been proven analytically. To the best of our knowledge and in the literature of the relay coupling system, no work has been carried out concerning the study of the stability of adaptive synchronization case. The Synchronization of the system is analysed in terms of its control gain by using time series. The numerical results show that there is global synchronization between the three relay coupled NHO-type oscillators for both non-adaptive and adaptive synchronizations. Moreover, PSpice based simulations of the analog electronic circuit for the non-adaptive case are in good accordance with both theoretical and numerical results.
Highlights
The idea of investigating the collective behavior of coupled dynamical systems has provoked a great deal of research efforts in the past two decades [1, 2]
Motivated by the above discussions and via periodically intermittent discrete observation control (PIDOC), we study the problem of synchronization in a relay configuration based on the coupling of three new three-component hyperchaotic oscillators (NHO) whose synchronization criteria are obtained with the help of Lyapunov method
Among the complex behaviours exhibited by this oscillator, we have limited our investigation to the set of parameters for which our oscillator presented a rich dynamic phenomenon intrinsic to neurons, characterized by alternating sequence of active states and passive states, and known as bursting oscillations
Summary
The idea of investigating the collective behavior of coupled dynamical systems has provoked a great deal of research efforts in the past two decades [1, 2]. We noted in the literature that the design of control scheme is often necessary to drive the synchronization of relay coupled systems To reach this synchronization, many control methods have been developed namely: the impulsive control [26], the feedback control [27], the periodically intermittent control [28], and so on. Motivated by the above discussions and via PIDOC, we study the problem of synchronization in a relay configuration based on the coupling of three new three-component hyperchaotic oscillators (NHO) whose synchronization criteria are obtained with the help of Lyapunov method.
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