Chaos in Kolmogorov systems with proliferation - general criteria and applications

We provide general criteria for existence of chaotic dynamics in Kolmogorov systems with proliferation. As applications, we provide a new proof of chaoticity of a class of constant coefficient birth-and-death systems and also show that a finite difference discretization of a class of drift diffusion equations generates chaotic dynamics. We also present a general method of constructing chaotic Kolmogorov systems.