Multiplicity of subharmonics in a class of periodic predator-prey Volterra models

TL;DR

This paper investigates the complex structure of subharmonic solutions in a periodic predator-prey model, revealing the existence of all orders of subharmonics and detailing their topological organization.

Contribution

It establishes the global topological structure of subharmonics in a predator-prey model and characterizes their bifurcation behavior using topological methods.

Findings

Existence of subharmonics of all orders for certain parameter ranges

Detailed topological structure of subharmonic components

Bifurcation analysis of the coexistence state

Abstract

This paper ascertains the global topological structure of the set of subharmonics of arbitrary order of the periodic predator-prey model introduced in L\'opez-G\'omez, Ortega and Tineo in 1996. By constructing the iterates of the monodromy operator of the system, it is shown that the system admits subharmonics of all orders for the appropriate ranges of values of the parameters. Then, some sharp results of topological nature in the context of global bifurcation theory provide us with the fine topological structure of the components of subharmonics emanating from the T-periodic coexistence state.