This paper investigates multiple bifurcations analyses and strong resonances of the Bazykin-Berezovskaya predator-prey model in depth using analytical and numerical bifurcation analysis.The stability conditions of fix...This paper investigates multiple bifurcations analyses and strong resonances of the Bazykin-Berezovskaya predator-prey model in depth using analytical and numerical bifurcation analysis.The stability conditions of fixed points,codim-1 and codim-2 bifurcations to include multiple and generic bifurcations are studied.This model exhibits transcritical,fip,Neimark-Sacker,and 1:2,1:3,1:4 strong resonances.The normal form coefficients and their scenarios for each bifurcation are examined by using the normal form theorem and bifurcation theory.For each bifurcation,various types of critical states are calculated,such as potential transformations between the one-parameter bifurcation point and different bifurcation points obtained from the two-parameter bifurcation point.To validate our analytical findings,the bifurcation curves of fixed points are determined by using MatcontM.展开更多
The positive connection between the total individual fitness and population density is called the demographic Allee effect.A demographic Allee effect with a critical population size or density is strong Allee effect.I...The positive connection between the total individual fitness and population density is called the demographic Allee effect.A demographic Allee effect with a critical population size or density is strong Allee effect.In this paper,discrete counterpart of Bazykin–Berezovskaya predator–prey model is introduced with strong Allee effects.The steady states of the model,the existence and local stability are examined.Moreover,proposed discrete-time Bazykin–Berezovskaya predator–prey is obtained via implementation of piecewise constant method for differential equations.This model is compared with its continuous counterpart by applying higher-order implicit Runge–Kutta method(IRK)with very small step size.The comparison yields that discrete-time model has sensitive dependence on initial conditions.By implementing center manifold theorem and bifurcation theory,we derive the conditions under which the discrete-time model exhibits flip and Niemark–Sacker bifurcations.Moreover,numerical simulations are provided to validate the theoretical results.展开更多
文摘This paper investigates multiple bifurcations analyses and strong resonances of the Bazykin-Berezovskaya predator-prey model in depth using analytical and numerical bifurcation analysis.The stability conditions of fixed points,codim-1 and codim-2 bifurcations to include multiple and generic bifurcations are studied.This model exhibits transcritical,fip,Neimark-Sacker,and 1:2,1:3,1:4 strong resonances.The normal form coefficients and their scenarios for each bifurcation are examined by using the normal form theorem and bifurcation theory.For each bifurcation,various types of critical states are calculated,such as potential transformations between the one-parameter bifurcation point and different bifurcation points obtained from the two-parameter bifurcation point.To validate our analytical findings,the bifurcation curves of fixed points are determined by using MatcontM.
文摘The positive connection between the total individual fitness and population density is called the demographic Allee effect.A demographic Allee effect with a critical population size or density is strong Allee effect.In this paper,discrete counterpart of Bazykin–Berezovskaya predator–prey model is introduced with strong Allee effects.The steady states of the model,the existence and local stability are examined.Moreover,proposed discrete-time Bazykin–Berezovskaya predator–prey is obtained via implementation of piecewise constant method for differential equations.This model is compared with its continuous counterpart by applying higher-order implicit Runge–Kutta method(IRK)with very small step size.The comparison yields that discrete-time model has sensitive dependence on initial conditions.By implementing center manifold theorem and bifurcation theory,we derive the conditions under which the discrete-time model exhibits flip and Niemark–Sacker bifurcations.Moreover,numerical simulations are provided to validate the theoretical results.
