Dynamical Stability Analysis Of Population With Stage Structure

Predation is common natural phenomena in ecosystem,and studying their interactions is of great significance for species diversity and sustainable survival.By constructing three kinds of differential equation models of population dynamics with stage structure,this paper discusses the positive and boundedness of the system solutions,analyzes the existence,stability and Hopf bifurcation of non-negative equilibrium points.Moreover,we consider the effects of prey group defense,hunting cooperation and vigilance,as well as fear carry-over effect and predator-taxis sensitivity on the dynamic behavior of prey-predator system with predator stage structure by numerical simulation.The main content of the full text is:1.The effects of stage structure and prey group defense on population dynamics behavior are studied.A prey-predator dynamic model with stage structure and prey group defense is constructed.On the basis of proving that the solutions of the system are non-negative and bounded,the existence of equilibrium points are analyzed,and then its local stability is discussed,and the numerical simulations of the model verifies our theoretical analysis.The results have shown that the smaller transition rate of juvenile to adult predators and the larger search efficiency of adult predator is beneficial to stability of the system.2.The effect of hunting cooperation induced vigilance on predator stage structure dynamics behavior are explored.A prey-predator dynamic model with stage structure that includes vigilance and hunting cooperation is proposed.The positivity and boundedness of the system solutions are proved,and its stability is discussed which is based on proving the existence of equilibrium points,then the threshold conditions which the Hopf bifurcation occurs are derived.It demonstrates that vigilance and hunting cooperation induce dynamics including stable state,Hopf bifurcation.It is found that with increasing of the vigilance the system undergoes transitions from periodic oscillation to the stable state,and even to predator extinction.3.The impact of fear carry-over effects and predator-taxis sensitivity on population dynamics behavior are considered.A prey-predator dynamic model with stage structure which includes fear carry-over effects and predator-taxis sensitivity is studied.It is proved that the solutions of the system are non-negative and bounded,and its local stability is discussed which is based on proving the existence of equilibrium points.The numerical simulation results show that the stronger fear effect and the weaker fear carry-over effect is beneficial to stability of the system,the appropriate predator-taxis sensitivity is conducive to species coexistence.