Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments

Abstract This article deals with the existence, multiplicity, minimal complexity, and global structure of subharmonic solutions to a class planar Hamiltonian systems periodic coefficients, being classical predator-prey model V. Volterra its most paradigmatic example. By means topological approach based on techniques from bifurcation theory, first part paper ascertains their nature, multiplicity as well structure, in terms configuration function coefficients setting model. The second introduces dynamical system theory horseshoes that permits detect, besides solutions, “chaotic-type” solutions. As byproduct our analysis, simplest prototype models environments can provoke chaotic dynamics. cannot occur cooperative quasi-cooperative dynamics, consequence ordering imposed by maximum principle.