Synchronization in Fractional-Order Complex-Valued Delayed Neural Networks

Abstract

This paper discusses the synchronization of fractional order complex valued neural networks (FOCVNN) at the presence of time delay. Synchronization criterions are achieved through the employment of a linear feedback control and comparison theorem of fractional order linear systems with delay. Feasibility and effectiveness of the proposed system are validated through numerical simulations.

Lyapunov Functions to Caputo Fractional Neural Networks with Time-Varying Delays

“…In this case we assume: Assumption 5. There exists a function ξ ∈ C(R + , R) such that for any solution x(t) of the FODNN (18) and any point t > 0 : ∑ n j=1 x 2 j (t) = sup s∈[−r,0] ∑ n j=1 x 2 j (s) and i = 1, 2, . .…”

“…Stability results concerning integer-order neural networks can be found in [7][8][9] and recently Lyapunov stability theory for fractional order systems was discussed (see [10,11]). Fractional order Lyapunov stability theory was applied for various types of fractional neural networks using quadratic Lyapunov functions (see [2,[12][13][14]) and stability analysis of fractional-order delay neural networks can be found in [15][16][17][18][19], for example. Finite-time stability of fractional-order neural networks with constant transmission delay and constant self-regulating parameters is studied in [20,21] and for distributed delays and constant self-regulating parameters see [22].…”

Research Frontier in Chaos Theory and Complex Networks

“…Compared with real-valued neural networks, synchronization of fractional-order complex-valued neural networks (FOCVNN) has more complicated properties and dynamical behaviors. The paper "Synchronization in fractional-order complex valued neural networks" by Zhang et al [6], discusses FOCVNN at the presence of a time delay. It designs an error-feedback controller using the comparison theorem of linear fractional-order systems with delay and a fractional inequality, which can be easily applied to achieve synchronization of FOCVNN with delay and improves the existing results.…”

Adaptive Synchronization of Fractional-Order Complex-Valued Neural Networks with Discrete and Distributed Delays

“…To the best of our knowledge, few investigations have been devoted to the control and information synchronization of FCVNNs with time delays in spite of its practical significance. In [ 36 , 53 ], the problem of synchronization of FCVNNs with discrete time delays is analyzed and sufficient conditions are provided. On the other hand, adaptive control, as an efficient control method, has been designed and successfully applied to fractional order neural networks [ 34 , 54 ].…”