Method for determining the Lyapunov exponent of a continuous model using the monodrome matrix

Marek Berezowski

Chaos, Solitons & Fractals, 2024, vol. 186, issue C

Abstract: The Lyapunov exponent is a measure of the sensitivity of a dynamic system to any changes and disturbances. It is therefore applicable in many fields of science, including physics, chemistry, economics, psychology, biology, medicine, and technology. Therefore, there is a need to have effective methods for determining the value of this exponent. In particular, it concerns the definition of its sign. The positive value of the Lyapunov exponent confirms the sensitivity of the system, especially when the system is chaotic. A negative value indicates the stability of the dynamic system being tested. The numerical value of the Lyapunov exponent indicates the degree of sensitivity of the dynamic system under study. Although the mathematical definition of the Lyapunov exponent is clear and simple, in practice determining its value is not a trivial matter, especially for continuous models. This paper presents a method for determining the Lyapunov exponent for continuous models. This method is based on the monodromy matrix. The work, for example, presents research on the following models of physical systems: the Van der Pol model with external forcing, the nonlinear mathematical pendulum model with external forcing and the Lorenz weather model.

Keywords: Lyapunov exponent; Dynamics; Chaos; Steady state; Trajectories; Limit cycle; Quasi-periodic; Oscillations (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008865

DOI: 10.1016/j.chaos.2024.115334

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