Abstract
In this work, we propose and study a new amensalism system with Allee effect on the first species. First, we investigate the existence and stability of all possible coexistence equilibrium points and boundary equilibrium points of this system. Then, applying the Sotomayor theorem, we prove that there exists a saddle-node bifurcation under some suitable parameter conditions. Finally, we provide a specific example with corresponding numerical simulations to further demonstrate our theoretical results.
Highlights
The interaction between two or more species has been a central problem in ecology and biology since the famous Lotka–Volterra model was proposed
The interaction between different species generates a complicated dynamics of biological species and exhibits the complexity and diversity
(1) If α = α2, the equilibrium point P31 is a saddle node, that is, Sε(P31) is divided into two parts by two separatrices that tend to P31 along the upside and the underneath of P31, where Sε(P31) is a neighborhood of P31 with sufficient small radius ε
Summary
The interaction between two or more species has been a central problem in ecology and biology since the famous Lotka–Volterra model was proposed. Α 2 –2α γ α and λ2(P1) = 1 > 0, so the equilibrium point P2 is a hyperbolic saddle This ends the proof of Theorem 2.2. (1) If α = α2, the equilibrium point P31 is a saddle node, that is, Sε(P31) is divided into two parts by two separatrices that tend to P31 along the upside and the underneath of P31, where Sε(P31) is a neighborhood of P31 with sufficient small radius ε. 2 in [27], we obtain that the equilibrium point P31 is a saddle node This means that a neighborhood Sε(P31) (ε is a sufficiently small radius) of P31 is divided into two parts by two separatrices that tend to P31 along the upside and the underneath of P31.
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