https://doi.org/10.1140/epjs/s11734-022-00447-3
Regular Article
On the boundedness and Lagrange stability of fractional-like neural network-based quasilinear systems
1
S.P. Timoshenko Institute of Mechanics, NAS of Ukraine, 03057, Kiev-57, Ukraine
2
Department of Mathematics, University of Texas at San Antonio, 78249, San Antonio, TX, USA
Received:
11
February
2021
Accepted:
13
January
2022
Published online:
25
January
2022
In this paper, a method for studying the boundedness of the solutions of Hopfield neural network systems with fractional-like derivatives (FLDs) is proposed. To this end, for quasilinear equations of perturbed motion with fractional-like derivatives of the state vectors, sufficient conditions for bounded solutions and Lagrange stability are established. These conditions are based on a new estimate of the Lyapunov function on the trajectories of the considered equations. Compare with the classical fractional-order derivatives, the notion of FLDs offers great computational simplifications related to FLDs of compositions of functions. The specific properties of the FLDs make the considered neural network model a new type of chaotic neural network with special features. The established results are also valid for systems where the order of the FLD is a time-varying function. In addition, it is important to note, that boundedness and Lagrange stability are qualitative properties with important applications in the study of periodicity and multi-stability of the systems.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2022
