We extend a previous Gause-type predator–prey model to include a general monotonic and bounded seasonally varying functional response. The model exhibits rich dynamical behaviour not encountered when the functional response is not seasonally forced. A theoretical analysis is performed on the model to investigate the global stability of the boundary equilibria and the existence of periodic solut...

In this paper, we consider the dynamics of a predator–prey system Gause type with cooperative hunting among predators and Holling III functional response. The known work numerically shows that exhibits saddle-node Hopf bifurcations except homoclinic bifurcation for some special parameter values. Our results show there are weak focus multiplicity three degenerate equilibrium double zero eigenval...

We study the existence of traveling wave solutions for a diffusive predator–prey system. The system considered in this paper is governed by a Sigmoidal response function which in some applications is more realistic than the Holling type I, II responses, and more general than a simplified form of the Holling type III response considered before. Our method is an improvement to the original method...

Cells, the basic units of organisms, consist of multiple essential elements such as carbon, nitrogen, and phosphorus. The scarcity of any of these elements can strongly restrict cellular and organismal growth. During recent years, ecological models incorporating multiple elements have been rapidly developed in many studies, which form a new research field of mathematical and theoretical biology...

In this article, we derive and analyze a novel predator–prey model with account for maturation delay in predators, ratio dependence, Holling type III functional response. The analysis of the system’s steady states reveals conditions on predation rate, predator growth time that can result prey-only equilibrium or facilitate simultaneous survival prey predators form stable coexistence state, sust...

The challenges to live in the open water and the diversity of habitats in the marine environments prompts phytoplankton to devise strategies which often involve production of toxins by Harmful Algal Bloom (HAB) and rapid production of metabolites from non-toxic precursor. The functional response of the predator is described by Holling type IV. We investigate wave phenomena and non-linear non-eq...