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Dynamic analysis of a slow-fast oscillator based on a coupled Duffing memristive system

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Abstract

The dynamic natural processes which occur in the world terrestrial system are highly nonlinear and exhibit unpredictable oscillations and behaviors. One way to imitate and follow the essential characteristics of these processes is a similar study of the nonlinear dynamics of two subsystems whose evolution is fast and slow, respectively. These dynamic systems are commonly used to describe various aspects of the dynamics of natural disasters in order to predict a solution. This article examines the dynamic properties and phenomena of a slow–fast 4D system consisting of the Duffing equation coupled to a proposed memristive system. The dynamics of the obtained system reveals the presence of multistability which is an unpredictable phenomenon whose different coexisting states must be quantified in order to adopt a means of control for better forecasting of disasters. Furthermore, the effect and strength of the coupling parameter on the interaction between the slow–fast dynamics of the subsystems is observed. Other dynamic properties such as offset boosting and bursting oscillations are also observed, further justifying the complexity of the system. An analog validation of the mathematical model is proposed through PSpice simulations of the corresponding electronic circuit, and the results sufficiently justify the feasibility.

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Funding

This research did not receive any specific grant from any funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Research Centre for Nuclear Science and Technology, Institute of Geological and Mining Research, P.O. Box 4110, Yaoundé, Cameroon

    Michaux Kountchou Noube & Vitrice Ruben Folifack Signing

  2. Unité de Recherche de Matière Condensée, d’Electronique et de Traitement du Signal (URMACETS), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon

    Hilaire Bertrand Fotsin

Authors
  1. Michaux Kountchou Noube
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  2. Vitrice Ruben Folifack Signing
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  3. Hilaire Bertrand Fotsin
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Contributions

M. Kountchou Noube: conceptualization, investigation, analysis, project administration, supervision, writing–review and editing; V.R. Folifack Signing: analysis, investigation, validation, visualization, writing–original draft, writing–review and editing; H.B. Fotsin: supervision, read and approved the final manuscript.

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Correspondence to Michaux Kountchou Noube.

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Kountchou Noube, M., Folifack Signing, V.R. & Fotsin, H.B. Dynamic analysis of a slow-fast oscillator based on a coupled Duffing memristive system. Int. J. Dynam. Control 11, 453–472 (2023). https://doi.org/10.1007/s40435-022-01011-6

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