Global Dynamics of a Class of Complex Valued Neural Networks

Abstract

In this paper activation dynamics of a complex valued neural network has been studied. Sufficient conditions for global exponential stability of a unique equilibrium are obtained. Our results show that in the serial mode of operation, the network converges to a stable state.

Global Stability of Complex-Valued Neural Networks on Time Scales

“…In Section 4, we derive new conditions that guarantee the global exponential stability of the equilibrium pattern for (1) on any arbitrary time scale. These conditions are new for the continuous case and improve known results even in the discrete case [10]. In Section 5, we present numerical examples for different choices of time scales.…”

“…6 Differ Equ Dyn Syst (Jan&Apr 2011) 19(1&2): [3][4][5][6][7][8][9][10][11] Lemma 2 Let y, f ∈ C rd and p ∈ R + . If y is differentiable on [t 0 , ∞) ∩ T such that…”

“…The following example is from [10]. We have applied this example to obtain results for a few well-known time scales.…”

“…The study of complex-valued neural networks (CVNNs for short) is a fast growing area of research in recent times as is apparent from a large number of publications (see e.g., [6][7][8]10,11] and the references therein). The main focus of these networks is aimed at exploring new capabilities and higher performance, making it possible to solve problems which cannot be solved with their real-valued counterparts.…”

“…Thus, the study of activation dynamics plays a significant role in the modeling of brain activities. In a recent paper by Rao and Murthy [10], the authors have studied global activation dynamics of a discrete CVNN and have obtained easily verifiable sufficient conditions for global exponential stability of the unique equilibrium pattern. It is known that discrete CVNNs follow a specific time scale.…”