A necessary and sufficient condition for global asymptotic stability of time-varying Lotka-Volterra predator-prey systems
The authors consider the time-varying Lotka-Volterra predator-prey system \[ \frac{dN}{dt}=(a+ch(t)-dh(t)N-bP)N,\quad \frac{dP}{dt}=(-c+dN)P,\eqno(E) \] \(N\) and \(P\) represent the prey population (or density) and the predator population (or density), respectively; the function \(h(t)\) is nonnegative, and \(a,b,c\) and \(d\) are positive constants. Necessary and sufficient conditions for the global asymptotic stability of the unique interior equilibrium \(x^*=(c/d, a/b)\) have been obtained in this paper.
scientific article; zbMATH DE number 6487756
scientific article