Abstract
Chaotic dynamics of numerous memristor-based circuits is widely reported in literature. Recently, some works have appeared which study the problem of synchronization control of these systems in a master-slave configuration. In the present paper, the spontaneous dynamic behavior of two chaotic memristor-based Chua’s circuits, mutually interacting through a coupling resistance, was studied via computer simulations in order to study possible self-organized synchronization phenomena. The used memristor is a flux controlled memristor with a cubic nonlinearity, and it can be regarded as a time-varying memductance. The memristor, in effect, retains memory of its past dynamic and any difference in the initial conditions of the two circuits results in different values of the corresponding memductances. In this sense, due to the memory effect of the memristor, even if coupled circuits have the same parameters they do not constitute two completely identical chaotic oscillators. As is known, for nonidentical chaotic systems, in addition to complete synchronizations (CS) other weaker forms of synchronization which provide correlations between the signals of the two systems can also occur. Depending on initial conditions and coupling strength, both chaotic and nonchaotic synchronization are observed for the system considered in this work.
Highlights
One of the most important topics of contemporary science focuses on the study of continuous and discrete dynamical systems [1,2,3], analysing their organization as nonlinear evolving structures [4,5,6] or as artificial agents in synthetic environments [7, 8]
The results obtained in the C-C and C-D cases qualitatively reproduce the entire phenomenology observed in all the simulations performed for this study, and only these two cases will be presented below in detail
The great sensitivity of the single circuit on initial conditions was here investigated by means of a bifurcations diagram for the maxima of the flux w(t) as a function of its initial values w(0)
Summary
One of the most important topics of contemporary science focuses on the study of continuous and discrete dynamical systems [1,2,3], analysing their organization as nonlinear evolving structures [4,5,6] or as artificial agents in synthetic environments [7, 8]. Since the actual memductance value depends on the history of the applied voltage, starting from different initial conditions the memristors in the two circuits have different memories, which results in different values of the memductance In this sense, despite having the same circuit parameters, the two circuits can be viewed as nonperfectly identical chaotic oscillators. A more general synchronization state, that seems to be the chaos synchrony most frequently found in natural systems [54], is the generalized synchronization (GS) It is characterized by a functional relationship between the trajectories of two coupled systems [55, 56], either identical or nonidentical. Generally speaking, chaos synchronization refers to a dynamic process in which two coupled chaotic systems adjust a given property of their motion to a common behavior, ranging from complete agreement of trajectories to a generic relationship between them.
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