Global solution curves for first order periodic problems, with applications

TL;DR

This paper investigates the global structure and multiplicity of periodic solutions in first-order periodic problems using continuation and bifurcation methods, with applications to population models and limit cycle stability.

Contribution

It introduces a comprehensive analysis of solution curves for first-order periodic problems, combining theoretical and numerical approaches, with specific applications to ecological models.

Findings

Identified multiple periodic solutions and their bifurcation points.

Mapped the global structure of solution curves.

Demonstrated stability of certain limit cycles in population models.

Abstract

Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for periodic problems of first order. The results are applied to a population model with fishing, and to the existence and stability of limit cycles. We also describe in detail our numerical computations of curves of periodic solutions, and of limit cycles.