The interaction between predators and preys exhibits more complicated behavior under the influence of crowding effects. By taking into account the crowding effects, the qualitative behavior of a prey-predator model is...The interaction between predators and preys exhibits more complicated behavior under the influence of crowding effects. By taking into account the crowding effects, the qualitative behavior of a prey-predator model is investigated. Particularly, we examine the boundedness as well as existence and uniqueness of positive steady-state and stability analysis of the unique positive steady-state. Moreover, it is also proved that the system undergoes Hopf bifurcation and flip bifurcation with the help of bifurcation theory. Moreover, a chaos control technique is proposed for controlling chaos under the influence of bifurcations. Finally, numerical simulations are provided to illustrate the theoretical results. These results of numerical simulations demonstrate chaotic long-term behavior over a broad range of parameters. The presence of chaotic behavior in the model is confirmed by computing maximum Lyapunov exponents.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The interaction between predators and preys exhibits more complicated behavior under the influence of crowding effects. By taking into account the crowding effects, the qualitative behavior of a prey-predator model is investigated. Particularly, we examine the boundedness as well as existence and uniqueness of positive steady-state and stability analysis of the unique positive steady-state. Moreover, it is also proved that the system undergoes Hopf bifurcation and flip bifurcation with the help of bifurcation theory. Moreover, a chaos control technique is proposed for controlling chaos under the influence of bifurcations. Finally, numerical simulations are provided to illustrate the theoretical results. These results of numerical simulations demonstrate chaotic long-term behavior over a broad range of parameters. The presence of chaotic behavior in the model is confirmed by computing maximum Lyapunov exponents.
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.
