We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R(4) and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R...

In this paper, a delayed Nicholson,s blowflies model with a linear harvesting term is investigated. Regarding the delay as a bifurcation parameter, we show that Hopf bifurcation will occur when the delay crosses a critical value. Numerical simulations supporting the theoretical findings are carried out. Keywords—Nicholson,s blowflies model; Stability; Hopf bifurcation; Delay.

The traditional SIRS virus propagation model is used to analyze the malware behavior of wireless rechargeable sensor networks (WRSNs) by adding a new concept: low-energy status nodes. SIRS-L has been developed in this article. Furthermore, influence time delay during charging nodes needs be considered. Hopf bifurcation studied discussing that chosen as parameter. Finally, properties are explore...

the predator-prey model with stage structure for predator is generalized in the context of ecoepidemiology, where the prey population is infected by a microparasite and the predator completely avoids consuming the infected prey. the intraspecific competition of infected prey is considered. all the equilibria are characterized and the existence of a hopf bifurcation at the coexistence equilibriu...

In this paper, the pattern formation of the attraction-repulsion Keller-Segel (ARKS) system is studied analytically and numerically. By the Hopf bifurcation theorem as well as the local and global bifurcation theorem, we rigorously establish the existence of time-periodic patterns and steady state patterns for the ARKS model in the full parameter regimes, which are identified by a linear stabil...

The hair bundle of sensory cells in the vertebrate ear provides an example of a noisy oscillator close to a Hopf bifurcation. The analysis of the data from both spontaneous and forced oscillations shows a strong violation of the fluctuation-dissipation theorem, revealing the presence of an underlying active process that keeps the system out of equilibrium. Nevertheless, we show that a generaliz...

       In this paper an SIS epidemic model with saturated incidence rate and treatment func- tion is proposed and studied. The existence of all feasible equilibrium points is discussed. The local stability conditions of the disease free equilibrium point and endemic equilibrium point are established with the help of basic reproduction number.However the global stabili- ty conditions of these eq...

This paper, according to the process of capital return, establishes a differential dynamics model investment with two time delays. When both delays are zero, it is proved that positively invariant, uniformly bounded, and globally asymptotically stable by using comparison principle Bendixson–Dulac theorem. at least one delay not Hopf bifurcation theorem, conditions local asymptotic stability exi...

Abstract Analytical determination of the bifurcation thresholds is of important interest for practical electrical machine design and analysis control. This paper presents mathematical investigation of the qualitative behavior of indirect filed oriented control induction motor based on bifurcation theory. In this context, steady-state responses analysis of the motor model is discussed and an ana...

In this paper, we study the existence of periodic orbits bifurcating from stationary solutions in a non-smooth planar dynamical system. This phenomenon is interpreted as generalized Hopf bifurcation. In the case of smoothness, Hopf bifurcation is characterized by a pair of complex conjugate eigenvalues crossing through the pure imaginary axis. This method does not apply to a non-smooth system d...