<p style='text-indent:20px;'>In this paper, we consider a predator-prey model with memory-based diffusion. We first analyze the stability of all steady states in detail. Then by analyzing distribution eigenvalues, find that average memory period can cause change positive state, and Hopf bifurcation occurs at state. Moreover, from central manifold theorem normal form theory, give direction...

We describe the qualitative dynamics and bifurcation set for a laser with injected signal for small cavity detunings. The main organizing center is the Hopf-saddle-node bifurcation from where a secondary Hopf bifurcation of a periodic orbit originates. We show that the laser’s stable cw solution existing for low injections, also suffers a secondary Hopf bifurcation. The resonance structure of b...

We study some periodic and quasiperiodic behaviors exhibited by the Chua’s equation with a cubic nonlinearity, near a Hopf–pitchfork bifurcation. We classify the types of this bifurcation in the nondegenerate cases, and point out the presence of a degenerate Hopf–pitchfork bifurcation. In this degenerate situation, analytical and numerical study shows a diversity of bifurcations of periodic orb...

We extend an investigation into the bifurcation phenomena exhibited by an oxidation reaction in an adiabatic reactor to the case of a diabatic reactor. The primary bifurcation parameter is the fuel fraction; the inflow pressure and inflow temperature are the secondary bifurcation parameters. The inclusion of heat loss in the model does not change the static steady-state bifurcation diagram; the...

This paper is devoted to the study of a spatially and age structured population dynamics model. We study the stability and Hopf bifurcation of the positive equilibrium of the model by using a bifurcation theory in the context of integrated semigroups. This problem is a first example for Hopf bifurcation for a spatially and age/size structured population dynamics model. Bifurcation analysis indi...

We consider an important class of non-symetric networks that lies between the class of general networks and the class of symmetric networks, where group theoretic methods still apply – namely, networks admitting “interior symmetries”. The main result of this paper is the full analogue of the Equivariant Hopf Theorem for networks with symmetries. We extend the result of Golubitsky, Pivato and St...

The stability and bifurcation analysis for a delay differential equation of hepatitis B virus infection is investigated. We show the existence of nonnegative equilibria under some appropriated conditions. The existence of the Hopf bifurcation with delay τ at the endemic equilibria is established by analyzing the distribution of the characteristic values. The explicit formulae which determine th...

Abstract: In this paper, a delayed ratio-dependent eco-epidemiological model with Holling type III functional response and two time delays is investigated.By regarding the delay as the bifurcation parameter, local stability of each equilibrium is discussed at the endemic equilibrium. By analyzing the corresponding characteristic equations, the conditions for existence of Hopf bifurcation for th...

Abstract. In this paper the dynamics of a three neuron model with self-connection and distributed delay under dynamical threshold is investigated. With the help of topological degree theory and Homotopy invariance principle existence and uniqueness of equilibrium point are established. The conditions for which the Hopf-bifurcation occurs at the equilibrium are obtained for the weak kernel of th...

In this paper, by using the Beurling-Nevanlinna type inequality we obtain new results on the existence of solutions of the Dirichlet problem with respect to the Schrödinger-prey operator. Meanwhile, the local stability of the Schrödingerean equilibrium and endemic equilibrium of the model are also discussed. We specially analyze the existence and stability of the Schrödingerean Hopf bifurcation...