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Organized periodic structures and coexistence of triple attractors in a predator–prey model with fear and refuge

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  • Garai, Shilpa
  • Pati, N.C.
  • Pal, Nikhil
  • Layek, G.C.

Abstract

We report the existence of periodic structures viz., Arnold tongues, and shrimp-shaped structures in the transitional and chaotic regimes in bi-parameter spaces of a predator–prey model. The model is constructed taking into consideration of two important effects: the prey refuge and fear of predation risk. The fixed points, their existence, and stability behaviors are analyzed. The occurrences of transcritical and Neimark–Sacker bifurcations are studied in both analytical and numerical approaches. The complex dynamical behaviors of the predator–prey model are explored in the bi-parameter space with the help of the largest Lyapunov exponent and isoperiodic diagrams. A completely new kind of U-shaped periodic structure has emerged by merging two Arnold tongues of the same period in the parameter plane. The transition to chaos also occurs through period-bubbling process. The coexistence of triple heterogeneous attractors indicates the unpredictability of the present deterministic model. The basin sets of triple coexisting attractors are drawn, and we observe the presence of Wada basin boundaries. Our studies reveal that the oscillations of the predator–prey populations in certain control parameter regions are highly dependent upon the initial densities of the populations.

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  • Garai, Shilpa & Pati, N.C. & Pal, Nikhil & Layek, G.C., 2022. "Organized periodic structures and coexistence of triple attractors in a predator–prey model with fear and refuge," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p2:s0960077922010128
    DOI: 10.1016/j.chaos.2022.112833
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    7. Hossain, Mainul & Pati, N.C. & Pal, Saheb & Rana, Sourav & Pal, Nikhil & Layek, G.C., 2021. "Bifurcations and multistability in a food chain model with nanoparticles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 808-825.
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