Stability and Hopf bifurcation analysis on a predator–prey model with discrete and distributed delays

Stability switches and Hopf bifurcations of an isolated population model with delay-dependent parameters

“…(4) Although much progress on the stability and Hopf bifurcation has been seen in various models with delay-independent parameters [31][32][33][34][35], a crucial point is that the dynamics of the systems differs dramatically if the corresponding characteristic equations involve the delay-dependent or the delay-independent coefficients. Most existing methods for studying the nonlinear dynamics fail when applied to the models with delay-dependent parameters.…”

“…(31) After finding the perturbed parameter values, we can write down the approximate solution of Eq. (6) as…”

Stability and Hopf bifurcation in a three-species system with feedback delays

“…In general, delay differential equations exhibit much more complicated dynamics than ordinary differential equations since a time delay could cause destabilization of the equilibrium. A great deal of research has been devoted to the delay models (see [8][9][10][11][12][13][14][15][16] and references therein).…”

Bifurcations in a predator-prey model with discrete and distributed time delay

“…Motivated by the work of Yan and Zhang [13], Ma et al [6] investigated the stability and Hopf bifurcation of the predator-prey model with discrete and distributed delays that takes the following form:…”

“…Based on the works [6,12,13], we consider the following predator-prey model with discrete time delay and distributed time delay:…”