In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given. Keyw...

In this paper, a nonlinear delay population model is investigated. Choosing the delay as a bifurcation parameter, we demonstrate that Hopf bifurcation will occur when the delay exceeds a critical value. Global existence of bifurcating periodic solutions is established. Numerical simulations supporting the theoretical findings are included. Keywords—Population model; Stability; Hopf bifurcation;...

We propose a biological economic model based on prey-predator dynamics where the prey species are continuously harvested and predation is considered with type II functional response. The dynamic behavior of the proposed biological economic prey-predator model is discussed. Continuous type gestational delay of predators is incorporated and its effect on the dynamical behavior of the model system...

We first consider the existence of local Hopf bifurcations, and then derive the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solutions, using the normal form theory and center manifold reduction. Further, particular attention is focused on the existence of the global Hopf bifurcation. By using the global Hopf bifurcation theory due to W...

We prove a Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations, which improves classical result by Crandall and Rabinowitz the case where basic are spaces. Actually, our does not need any compactness conditions, leads to wider applications. In particular, can be applied equations unbounded domains of $$\mathbb {R}^n$$ .

A three-dimensional bio-reactor model of exploitative competition of two predator organisms with inhibition responses for the same renewable organism with reproductive properties is considered. By using a Lyapunov function and the center manifold theorem the global stability, the existence of Hopf bifurcation and limit cycles are proved. This result is useful in understanding the nonlinear osci...

in this paper, a bidirectional associative memory (bam) neural network, which consists of two neurons in the x-layer and three neurons in the y-layer, with two time delays will be studied. we conclude that under some assumptions, hopf bifurcation occurs when the sum of two delays passes through a critical value. a numerical example is presented to support our theoretical results.

Abstract A diffusive phytoplankton–zooplankton model with nonlinear harvesting is considered in this paper. Firstly, using the as parameter, we get existence and stability of positive steady state, also investigate spatially homogeneous inhomogeneous periodic solutions. Then, by applying normal form theory center manifold theorem, give direction Hopf bifurcation from state. In addition, prove B...