The goal of this work is to formulate a general Holling-type functional, or behavioral, response for continuous physiologically structured populations, where both the predator and the prey have physiological densities and certain rules apply to their interactions. The physiological variable can be, for example, a development stage, weight, age, or a characteristic length. The model leads to a F...

In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a condition for diffusive instability of a locally stable equilibrium. Furthermore, we present a theoretical analysis of processes of pattern formation that invol...

The existence of positive periodic solutions for a delayed discrete predator-prey model with Holling-type-III functional responseN1(k+1)=N1(k)exp{b1(k)−a1(k)N1(k− [τ1]) −α1(k)N1(k)N2(k)/(N 1 (k) +m2N 2 (k))}, N2(k + 1) = N2(k)exp{−b2(k) + α2(k)N 1 (k − [τ2])/(N 1 (k − [τ2]) + m2N 2 (k − [τ2]))} is established by using the coincidence degree theory. We also present sufficient conditions for the ...

A diffusive predator-prey model with modified Leslie-Gower and Holling type IV schemes is investigated analytically and numerically. Mathematical theoretical works mainly focus on the existence of traveling wave solutions. Numerical simulations are performed to confirm the feasibility of traveling wave solutions. All these results are significant in exploration of the dynamic complexity of ecos...

In this paper, the general framework for calculating stability of equilibria, Hopf bifurcation a delayed prey-predator system with an SI type disease in prey population, is investigated. The impact incubation period delay on transmission utilizing nonlinear incidence rate was taken into account. For purpose explaining predation process, modified Holling II functional response used. First, exist...

In this paper, by incorporating the general delay to reaction term in memory-based diffusive system, we propose a system with memory and (e.g., digestion, gestation, hunting, migration maturation delays, etc.). We first derive an algorithm for calculating normal form of Hopf bifurcation proposed system. The developed can be used investigate direction stability bifurcation. As real application, ...