Bifurcations and chaotic analysis in a discrete predator-prey model with Ricker map

This paper delves into the intricate dynamics of a discrete predator-prey model of the Ricker map, which represents one of the most ubiquitous symbiotic relationships among natural populations. Known work studied the stability of the fixed points and gave all codimension-one bifurcations but no further discussion for codimension-two. In this paper, we investigate the codimension-two bifurcations associated with 1:2, 1:3, and 1:4 resonances. Furthermore, we examine the existence of chaos in the sense of Marotto. The numerical simulations are conducted to verify the theoretical findings and show the periodic behaviors of the system. The occurrence of resonances suggests that predator and prey populations experience periodic or quasi-periodic fluctuations, long-period fluctuations, large-scale population outbreaks, and even chaos when parameters vary.