Computer system organization

Features of the computational implementation of the algorithm for estimating the Lyapunov exponents of systems with delay

V. E. Goryunov

P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150003, Russia

Abstract: We consider the computational implementation of the algorithm for Lyapunov exponents spectrum numerical estimation for delay differential equations. It is known that for such systems, as well as for boundary value problems, it is not possible to prove the well-known Oseledets theorem which allows us to calculate the required parameters very efficiently. Therefore, we can only talk about the estimates of the characteristics in some sense close to the Lyapunov exponents. In this paper, we propose two methods of linearized systems solutions processing. One of them is based on a set of impulse functions, and the other is based on a set of trigonometric functions. We show the usage flexibility of these algorithms in the case of quasi-stable structures when several Lyapunov exponents are close to zero. The developed methods are tested on a logistic equation with a delay, and these tests illustrate the “proximity” of the obtained numerical characteristics and Lyapunov exponents.

Keywords: Lyapunov exponents spectrum, dynamical system with delay, numerical algorithm, Hutchinson equation.

UDC: 004.021, 517.929

Received: 23.10.2019
Revised: 06.11.2019
Accepted: 27.11.2019

DOI: 10.18255/1818-1015-572-582