Fixed time synchronization of delayed fractional memristive Hopfield neural networks and its fractal dimension analysis.

Abstract

In this article, the fixed time synchronization of fractional memristive Hopfield neural networks with constant delay is investigated using two different feedback controllers. Of proposed two controllers, first one follows the existing fixed time stability result and the second follows the newly derived fixed time stability theorem. The newly developed stability theorem is derived using certain inequality and variable substitution techniques. The stability criterion and expression for the new settling time's upper bound differ from those in the previously presented theorems. To demonstrate the effectiveness, numerical simulations are performed by considering two-dimensional drive-response systems. The results illustrate that the new settling time formula associated with the second controller is tighter than the existing settling time formula associated with the first controller. Further, the fractal dimension estimation of drive-response systems compares the irregularity based on the controllers.