Teacher:In this task, you're given a paragraph and title from the research paper. Your task is to classify whether the given title is suitable or not for the research paper based on the given paragraph. Return "True" if title is proper according to paragraph else "False".
Teacher: Now, understand the problem? Solve this instance: Paragraph: In this paper, we propose and analyze a nonautonomous predator-prey model with disease in prey, and a discrete time delay for the incubation period in disease transmission. Employing the theory of differential inequalities, we find sufficient conditions for the permanence of the system. Further, we use Lyapunov's functional method to obtain sufficient conditions for global asymptotic stability of the system. We observe that the permanence of the system is unaffected due to presence of incubation delay. However, incubation delay affects the global stability of the positive periodic solution of the system. To reinforce the analytical results and to get more insight into the system's behavior, we perform some numerical simulations of the autonomous and nonautonomous systems with and without time delay. We observe that for the gradual increase in the magnitude of incubation delay, the autonomous system develops limit cycle oscillation through a Hopf-bifurcation while the corresponding nonautonomous system shows chaotic dynamics through quasiperiodic oscillations. We apply basic tools of non-linear dynamics such as Poincare section and maximum Lyapunov exponent to confirm the chaotic behavior of the system.
Title: Chaos in a nonautonomous eco-epidemiological model with delay
Student:
True