A generalization of Lotka–Volterra, GLV, systems with some dynamical and topological properties

It is shown that local asymptotic instability is related to the existence of a positive Lyapunov exponent which is a necessary condition for chaos. Also it is proved that linear transformations do not affect the dynamical behaviour of the system. A generalized Lotka–Volterra (GLV) model is introduced and proved that for specific choices of parameters it exhibits chaos. Knots and links which arise from the system which describe the behaviour of a typical nuclear spin are studied. We conjecture that knots and links associated GLV is much more general than Lorenz knots, and the one predator – two preys LV model exhibits chaos for general parameters.