In this paper, the kinetics of a class delayed reaction-diffusion mussel-algae system under Neumann boundary conditions with half-saturation constant is studied. The global existence and priori bounds as well positive equilibrium are obtained. affects stability may result in Turing instability. When exceeds certain critical value, globally asymptotically stable which means that larger forces mu...

Using a drift flux representation for the two-phase flow, a new reduced order model has been developed to simulate density-wave oscillations (DWOs) in a heated channel. This model is then used to perform stability and semi-analytical bifurcation analysis, using the bifurcation code BIFDD, in which the stability boundary (SB) and the nature of Hopf bifurcation are determined in a suitable two-di...

Abstract— Papers investigate a Kaldor-Kalecki model of business cycle system with two different delays, which described the interaction of the gross product Y and the capital product K . We derived the conditions for the local stability and the existence of Hopf bifurcation at the equilibrium of the system. By applying the normal form theory and center manifold theory, some explicit formulate f...

A delayed three-species food chain system with two types of functional responses, Holling type and Beddington–DeAngelis type, is investigated. By analyzing the distribution of the roots of the associated characteristic equation, we get the sufficient conditions for the stability of the positive equilibrium and the existence of Hopf bifurcation. In particular, the properties of Hopf bifurcation ...

We analyze a differential-algebraic biological economic system with time delay. The model has two different Holling functional responses. By considering time delay as bifurcation parameter, we find that there exists stability switches when delay varies, and the Hopf bifurcation occurs when delay passes through a sequence of critical values. Furthermore, we also consider the stability and direct...

Three-species food-chain models, in which the prey population exhibits group defense, are considered. Using the carrying capacity of the environment as the bifurcation parameter, it is shown that the model without delay undergoes a sequence of Hopf bifurcations. In the model with delay it is shown that using a delay as a bifurcation parameter, a Hopf bifurcation can also occur in this case. The...

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich. The neural system exhibits a unique rest point or three ones for the different values of coupling strength by employing t...

In this paper we numerically study the properties and stability of the travelling combustion waves in Zeldovich-Liñán model in the adiabatic limit in one-dimension. The structure and the properties of the combustion waves are found to be different for the fast and slow recombination regimes. The dependence of flame speed on the parameters of the model are studied in detail. The results are comp...

In this paper, dynamical analysis is presented for a group of unicycles in leader-follower formation. The equilibrium formations were characterized along with the local stability analysis. It was demonstrated that with the variation in control gain, the collective dynamics might undergo Andronov-Hopf and Fold-Hopf bifurcations. An increase in the number of unicycles increase the vigor of quasi-...

This paper investigates the time delayed nonautonomous predator-prey models. The cause of the time delay considered here is due to gestation on the consumption of an infected prey by the predator. The local stability conditions are obtained by linearizing the models around the equilibrium points. Also the occurrence of Hopf bifurcation is proven analytically, corroborated with the computational...