The spatially homogeneous hopf bifurcation induced jointly by memory and general delays in a diffusive system

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, consider predator-prey model ratio-dependent Holling type-3 functional response, which includes gestation delays. analysis without is studied, then delays studied. By using bifurcation, supercritical stable spatially homogeneous periodic solutions induced jointly are found. also found numerical simulations confirms our analytic result.