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

Abstract

In this paper, the synchronization problem of fractional-order complex-valued neural networks with discrete and distributed delays is investigated. Based on the adaptive control and Lyapunov function theory, some sufficient conditions are derived to ensure the states of two fractional-order complex-valued neural networks with discrete and distributed delays achieve complete synchronization rapidly. Finally, numerical simulations are given to illustrate the effectiveness and feasibility of the theoretical results.

Keywords: complex-valued information; delay; fractional-order; neural networks; synchronization.

Figure 1

Time evolution of states $x_1$, $x_2$, $y_1$ and $y_2$ in 2-D plane.

Figure 2

Time evolution of $x_1$, $x_2$, $y_1$ and $y_2$ in 3-D space.

Figure 3

Synchronization errors $e_i\left(t\right)=y_i\left(t\right)-x_i\left(t\right)$ with five different initial values, $i=1,2$.

Figure 4

Synchronization errors $e_3^u\left(t\right)$ and $e_3^v\left(t\right)$ with five different initial values.

Figure 5

Time revolution of system (6) and (7) with controllers as Equation (11).

Figure 6

Time response of the feedback gains $d_i\left(t\right)$, $p_i\left(t\right)$, ${\eta }_i\left(t\right)$, ${\theta }_i\left(t\right)$ and $w_i\left(t\right)$.