This paper deals with the fractional neutral evolution differential inclusions. The existence results are established by using the fractional power of operators and a fixed point theorem for multivalued map. Moreover, we present a new generalized Gronwall inequality with singularity, which is an important tool in the proof of solvability.
This work investigates a prey–predator model with Beddington–DeAngelis functional response and discrete time delay in both theoretical and numerical ways. Firstly, we incorporate into the system a discrete time delay between the capture of the prey by the predator and its conversion to predator biomass. Moreover, by taking the delay as a bifurcation parameter, we analyze the stability of the positive equilibrium in the delayed system. We analytically prove that the local Hopf bifurcation critical values are neatly paired, and each pair is joined by a bounded global Hopf branch. Also, we show that the predator becomes extinct with an increase of the time delay. Finally, before the extinction of the predator, we find the abundance of dynamical complexity, such as supercritical Hopf bifurcation, using the numerical continuation package DDE-BIFTOOL.
This article is devoted to the dynamical behavior of a stochastic modified Bazykin predator–prey model under regime switching. Some sufficient conditions are derived to guarantee the asymptotic properties, persistent and extinct of solutions by using the stochastic comparison theorem, Itô formula and exponential martingale inequality. At last, some simulations are given to illustrate our main results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.