Input-to-state stability of memristor-based complex-valued neural networks with time delays

Input-to-state stability of delayed memristor-based inertial neural networks via non-reduced order method

This paper is concerned with the input-to-state stability (ISS) for a kind of delayed memristor-based inertial neural networks (DMINNs). Based on the nonsmooth analysis and stability theory, novel delay-dependent and delay-independent criteria on the ISS of DMINNs are obtained by constructing different Lyapunov functions. Moreover, compared with the reduced order approach used in the previous works, this paper consider the ISS of DMINNs via non-reduced order approach. Directly analysis the model of DMINNs can better maintain its physical backgrounds, which reduces the complexity of calculations and is more rigorous in practical application. Additionally, the novel proposed results on the ISS of DMINNs here incorporate and complement the existing studies on memristive neural network dynamical systems. Lastly, a numerical example is provided to show that the obtained criteria are reliable.

Stability Analysis for Memristor-Based Complex-Valued Neural Networks with Time Delays

In this paper, the problem of stability analysis for memristor-based complex-valued neural networks (MCVNNs) with time-varying delays is investigated extensively. This paper focuses on the exponential stability of the MCVNNs with time-varying delays. By means of the Brouwer's fixed-point theorem and M-matrix, the existence, uniqueness, and exponential stability of the equilibrium point for MCVNNs are studied, and several sufficient conditions are obtained. In particular, these results can be applied to general MCVNNs whether the activation functions could be explicitly described by dividing into two parts of the real parts and imaginary parts or not. Two numerical simulation examples are provided to illustrate the effectiveness of the theoretical results.

Memristor standard cellular neural networks computing in the flux-charge domain

The paper introduces a class of memristor neural networks (NNs) that are characterized by the following salient features. (a) The processing of signals takes place in the flux-charge domain and is based on the time evolution of memristor charges. The processing result is given by the constant asymptotic values of charges that are stored in the memristors acting as non-volatile memories in steady state. (b) The dynamic equations describing the memristor NNs in the flux-charge domain are analogous to those describing, in the traditional voltage-current domain, the dynamics of a standard (S) cellular (C) NN, and are implemented by using a realistic model of memristors as that proposed by HP. This analogy makes it possible to use the bulk of results in the SCNN literature for designing memristor NNs to solve processing tasks in real time. Convergence of memristor NNs in the presence of multiple asymptotically stable equilibrium points is addressed and some applications to image processing tasks are presented to illustrate the real-time processing capabilities. Computing in the flux-charge domain is shown to have significant advantages with respect to computing in the voltage-current domain. One advantage is that, when a steady state is reached, currents, voltages and hence power in a memristor NN vanish, whereas memristors keep in memory the processing result. This is basically different from SCNNs for which currents, voltages and power do not vanish at a steady state, and batteries are needed to keep in memory the processing result.