Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks

Changjin Xu, Maoxin Liao, Peiluan Li and Shuai Yuan

Chaos, Solitons & Fractals, 2021, vol. 142, issue C

Abstract: During the past decades, integer-order complex-valued neural networks have attracted great attention since they have been widely applied in in many fields of engineering technology. However, the investigation on fractional-order complex-valued neural networks, which are more appropriate to characterize the dynamical nature of neural networks, is rare. In this manuscript, we are to consider the stability and the existence of Hopf bifurcation of fractional-order complex-valued neural networks. By separating the coefficients and the activation functions into their real and imaginary parts and choosing the time delay as bifurcation parameter, we establish a set of sufficient conditions to ensure the stability of the equilibrium point and the existence of Hopf bifurcation for the involved network. The study shows that both the fractional order and the leakage delay have an important impact on the stability and the existence of Hopf bifurcation of the considered model. Some suitable numerical simulations are implemented to illustrate the pivotal theoretical predictions. At last, we ends this article with a simple conclusion.

Keywords: Complex-valued neural networks; Hopf bifurcation; Leakage delay; Stability; Fractional order (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920309279

DOI: 10.1016/j.chaos.2020.110535

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