On peaks in carrying simplices
نویسنده
چکیده
A necessary and sufficient condition is given for the carrying simplex of a dissipative totally competitive system of three ordinary differential equations to have a peak singularity at an axial equilibrium. For systems of Lotka–Volterra type that result translates into a simple condition on the coefficients.
منابع مشابه
Geometry of carrying simplices of 3-species competitive Lotka-Volterra systems
We investigate the existence, uniqueness and Gaussian curvature of the invariant carrying simplices of 3 species autonomous totally competitive Lotka-Volterra systems. Explicit examples are given where the carrying simplex is convex or concave, but also where the curvature is not single-signed. Our method monitors the curvature of an evolving surface that converges uniformly to the carrying sim...
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