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BIFURCATION ANALYSIS AND CHAOS CONTROL OF THE DISSOLVED OXYGEN-PHYTOPLANKTON DYNAMICAL MODEL

Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram 624 302, Tamil Nadu, India

E-mail Address: priyankamurugangri@gmail.com

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and

P. MUTHUKUMAR

https://orcid.org/0000-0003-1396-9948

Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram 624 302, Tamil Nadu, India

E-mail Address: pmuthukumargri@gmail.com

Corresponding author.

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https://doi.org/10.1142/S0218339024500347Cited by:0 (Source: Crossref)

Abstract

The production of oxygen through phytoplankton photosynthesis is a crucial phenomenon in the dynamics of marine ecosystems. A generic oxygen-phytoplankton interaction model is considered to comprehend its underlying mechanism. This paper investigates the discrete-time dynamics of oxygen and phytoplankton in aquatic ecosystems, incorporating factors that cause phytoplankton mortality due to external influences. We explore the conditions for the local stability of steady states concerning the oxygen content in dissolved water and phytoplankton density. The analysis reveals that the model undergoes a co-dimension one bifurcation, encompassing flip and Neimark–Sacker bifurcations, utilizing the center manifold theorem and bifurcation theory. To manage the chaos resulting from the Neimark–Sacker bifurcation, we apply the OGY feedback control method and a hybrid control methodology. Finally, we present numerical simulations to validate the theoretical discussion.

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