On Flows of Neural Ordinary Differential Equations That Are Solutions of Lotka-Volterra Dynamical Systems

Periodic Solutions of Periodic Delay Lotka Volterra Equations and Systems

By using the continuation theorem of coincidence degree theory, sufficient and realistic conditions are obtained for the existence of positive periodic solutions for both periodic Lotka Volterra equations and systems with distributed or statedependent delays. Our results substantially extend and improve existing results. 2001 Academic Press

Dynamical behaviour of Lotka-Volterra systems

We consider the (n 1)-dimensional Lotka-Volterra system (arising in biological modelling of species interactions), and associate with it a family of n-dimensional systems having the same phase portrait. We obtain some results on global behaviour and convergence towards the equilibrium in the case where the LV system is “nearly symmetric” or “nearly cooperative” (that is, there exists a member o...

Ordinary Differential Equations and Dynamical Systems

Ordinary Differential Equations and Dynamical Systems

This manuscript provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore we consider linear equations, the Floquet theorem, and the autonomous...

Volterra integro-differential equations and infinite systems of ordinary differential equations