https://doi.org/10.1140/epjs/s11734-024-01196-1
Regular Article
Bifurcation analysis of a discrete-time coral reef model with growth rate on macroalgae
Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, 624302, Dindigul, Tamil Nadu, India
Received:
17
March
2024
Accepted:
4
June
2024
Published online:
19
June
2024
The reduction in coral reef densities, characterized by the proliferation of macroalgae, has emerged as a global threat. Here, we consider a discrete-time coral reef model under the assumption that a particular region of the seabed is covered entirely by macroalgae (M), coral (C), and algal turfs (T). We explore all ecologically possible equilibrium points and analyze the conditions for their local stability. Our analysis reveals that the model undergoes co-dimension one period-doubling bifurcation. Finally, we provide numerical simulations to validate the results and demonstrate the complex dynamic behaviors that arise, including reversal period-doubling bifurcation, period 4, 8, and 24 bubble bifurcations, and chaotic behavior.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.