Hopf bifurcation

Dynamics of a diffusive business cycle model with two delays and variable depreciation rate

The main aim of this work is to analyze the dynamics of a delayed business cycle model described by partial differential equations (PDEs) in order to take into account the depreciation rate of capital stock and the diffusion effect.  Firstly, the existence of solutions and the economic equilibrium are carefully studied.  Secondly, the local stability and the existence of Hopf bifurcation are established.  Finally, some numerical simulations are presented to illustrate the analytical results.

A generalized diffusive IS-LM business cycle model with delays in gross product and capital stock

In this paper, we suggest a diffusive and delayed IS-LM business cycle model with interest rate, general investment and money supply under homogeneous Neumann boundary conditions.  The time delays are respectively incorporated into capital stock and gross product.  We first demonstrate the model's sound mathematical and economic posing.  By examining the corresponding characteristic equation, the local stability of the economic equilibrium and the existence of Hopf bifurcation are proved.

Mathematical analysis of a spatiotemporal dynamics of a delayed IS-LM model in economics

The purpose of this research is to suggest and analyze a spatiotemporal of an IS-LM model with two delays, interest rate, liquidity preference and general investment function.  The first delay into the proposed model refers to the time delay between the decision of investment and his implementation.  However, the second one represents the delay in investment production.  The well posedness of the model is proved.  The stability analysis and the existence of Hopf bifurcation are obtained.  Furthermore, numerical examples that confirm the analytical results are shown.

Stability analysis and Hopf bifurcation of a delayed prey–predator model with Hattaf–Yousfi functional response and Allee effect

The Allee effect is an important phenomena in the context of ecology characterized by a correlation between population density and the mean individual fitness of a population.  In this work, we examine the influences of Allee effect on the dynamics of a delayed prey–predator model with Hattaf–Yousfi functional response.  We first prove that the proposed model with Allee effect is mathematically and ecologically well-posed.  Moreover, we study the stability of equilibriums and discuss the local existence of Hopf bifurcation.

Study of Hopf bifurcation of delayed tritrophic system: dinoflagellates, mussels, and crabs

In this paper, we have a discrete delayed dynamic system of three marine species: prey, predator, and superpredator.  In addition to the effect of prey toxicity, we consider the negative fishing effect of these species.  The study of this model consists of the search for equilibria with eigenvalue analysis, the existence of Hopf bifurcations at interior equilibria, and the determination of direction and stability analysis of Hopf bifurcation using the theory of normal form and center manifold.  Some examples are given with numerical simulations to illustrate the results

Carbon monoxide oxidation on the Pt-catalyst: modelling and stability

A two-dimensional mathematical model of carbon monoxide (CO) oxidation is investigated for the Langmuir-Hinshelwood mechanism on the surface of a Platinum (Pt) catalyst. The adsorbate-driven structural phase transition of catalytic surface is taken into account. The stability analysis of the model solutions is carried out. It is shown that the spatio-temporal periodic chemical oscillations of CO and oxygen (O) surface coverages and a fraction of the surface in the non-reconstructed $(1\times 1)$-structure occur. Conditions for Hopf and Turing bifurcation to arise are investigated.