On the nonautonomous N-competing species problems

Abstract

We consider a nonautonomous system of ordinary differential equations which models competition among n species. Conditions are given under which there exists a unique solution with components bounded above and below by positive constants on (-∞, ∞) and which attracts all other solutions with positive components. In the case where this system is periodic or almost periodic in time, this unique solution is periodic or almost periodic. Our proofs make use of a combination of techniques from [6] and [8] and improve the results of these papers. An example is given to illustrate this improvement and another example shows that certain conditions which imply existence do not imply the conditions guaranteeing uniqueness and stability.

Keywords:

• Lyapunov function
• globally attracting solution

Additional information

Notes on contributors

Shair Ahmad