Nonlinear Dynamics

, Volume 95, Issue 2, pp 1269–1282 | Cite as

Effects of initial conditions on the synchronization of the coupled memristor neural circuits

  • Jihong Zhang
  • Xiaofeng LiaoEmail author
Original Paper


The fourth basic two-terminal circuit element has been called the memristor because its resistance (conductance) depends on the complete past history of the memristor current (voltage), i.e., the initial charge (flux) condition at a given instant. This paper aims to provide some insight into the effects of the initial flux condition of the memristor synapse in the synchronization of two coupled memristor-based neural circuits. First, we build the coupled memristor-based FitzHugh–Nagumo circuits with the memristor synapse, and obtain the initial conditions by means of the flux-charge analysis method in the differential equations. Then, as a result of varying the initial conditions of the coupling memristor in the neural network, the details of synchronization with the parallel shift are derived theoretically by solving the nonhomogeneous error equations. These results of theoretical analyses have been confirmed by numerical simulations. Finally, we focus on the influence of the initial condition of the memristor on chaos generation for individual FitzHugh–Nagumo neuron and how to change chaotic state into stable periodic oscillation for a FitzHugh–Nagumo neuron in the synchronous neural network.


Initial flux condition Memristor synapse FitzHugh–Nagumo circuit Synchronization Coupled neural network 



This work was supported in part by the National Key Research and Development Program of China under Grant 2016YFB0800601, in part by the National Natural Science Foundation of China under Grant 61472331 and 61772434.

Compliance with ethical standards

Conflict of interest

The authors declare that there are no conflicts of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information EngineeringSouthwest UniversityChongqingPeople’s Republic of China

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