Dynamic Behaviors of an Obligate Commensal Symbiosis Model with Crowley–Martin Functional Responses

Xu, Lili; Xue, Yalong; Xie, Xue‐Jun; Qi, Lin

doi:10.3390/axioms11060298

Cited by 8 publications

(1 citation statement)

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“…A symbiotic relationship in an ecosystem is a relatively close interrelationship between individuals of different species that can generally increase the fitness of one or both parties. It primarily includes mutualism, commensalism, and amensalism (see [1][2][3][4][5][6][7][8] and references therein). Amensalism refers to the interaction of two species in which only one side is restricted and restrained, while the other side is unaffected.…”

Section: Introductionmentioning

confidence: 99%

Complex Dynamics Analysis of a Discrete Amensalism System with a Cover for the First Species

Zhou¹,

Chen²,

Lin³

2022

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Of interest is the dynamics of the discrete-time amensalism model with a cover on the first species. We first obtain the existence and stability of fixed points and the conditions for the permanent coexistence of two species. Then we demonstrate the occurrence of flip bifurcation by using the central manifold theorem and bifurcation theory. A hybrid control strategy is used to control the flip bifurcation and stabilize unstable periodic orbits embedded in the complex attractor. Numerical simulation verifies the feasibility of theoretical analysis and reveals some novel and exciting dynamic phenomena.

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