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 study of the population dynamics of a three-species Lotka-Volterra model is crucial in gaining a deeper understanding of the delicate balance between prey and predator populations.This research takes a unique appr...The study of the population dynamics of a three-species Lotka-Volterra model is crucial in gaining a deeper understanding of the delicate balance between prey and predator populations.This research takes a unique approach by exploring the stability of fixed points and the occurrence of Hopf bifurcation.By using the bifurcation theory,our study provides a comprehensive analysis of the conditions for the existence of Hopf bifurcation.This is validated through detailed numerical simulations and visual representations that demonstrate the potential for chaos in these systems.To mitigate this instability,we employ a hybrid control strategy that ensures the stability of the controlled model even in the presence of Hopf bifurcation.This research is not only significant in advancing the field of ecology but also has far-reaching practical implications for wildlife management and conservation efforts.Our results provide a deeper understanding of the complex dynamics of prey-predator interactions and have the potential to inform sustainable management practices and ensure the survival of these species.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 study of the population dynamics of a three-species Lotka-Volterra model is crucial in gaining a deeper understanding of the delicate balance between prey and predator populations.This research takes a unique approach by exploring the stability of fixed points and the occurrence of Hopf bifurcation.By using the bifurcation theory,our study provides a comprehensive analysis of the conditions for the existence of Hopf bifurcation.This is validated through detailed numerical simulations and visual representations that demonstrate the potential for chaos in these systems.To mitigate this instability,we employ a hybrid control strategy that ensures the stability of the controlled model even in the presence of Hopf bifurcation.This research is not only significant in advancing the field of ecology but also has far-reaching practical implications for wildlife management and conservation efforts.Our results provide a deeper understanding of the complex dynamics of prey-predator interactions and have the potential to inform sustainable management practices and ensure the survival of these species.
