Revisiting Comins, Hassell, and May

TL;DR

This paper revisits early 1990s research on Nicholson-Baily dynamics with modern computational tools, revealing that various spatial behaviors are part of a spectrum and introducing a Lyapunov spectrum sampling method for bifurcation analysis.

Contribution

It develops a new sampling technique for Lyapunov spectra, unifies different spatial behaviors into a spectrum, and provides deeper insights into crystalline structures and bifurcations.

Findings

Spatial chaos, spirals, and hard-to-start spirals form a continuum of behaviors.

Lyapunov sampling effectively identifies bifurcation curves.

Discovery of an interesting spatial chimera pattern.

Abstract

In a sequence of papers in the early 1990's, Comins, Hassell, and May investigated Nicholson-Baily dynamics in a spatial implementation with diffusion. They delineated four types of dynamic behavior: crystalline lattices, spatial chaos, spirals, and hard-to-start spirals. We revisit their results with current computational methods, and develop a sampling technique to estimate the Lyapunov spectrum. We find that spatial chaos, spirals, and hard-to-start spirals are not separate categories, but part of a spectrum of behavior. We more thoroughly investigate the crystalline structures. We show that the Lyapunov sampling method can be used to find bifurcation curves in parameter space, and demonstrate an interesting spatial chimera.