Stability and Hopf Bifurcation Analysis on a Nonlinear Business Cycle Model

Hopf bifurcation of the stochastic model on business cycle

Hopf bifurcation analysis of a diffusive predator-prey model with Monod-Haldane response

In this paper, we have studied the diffusive predator-prey model with Monod-Haldane functional response. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. We also study the spatially homogeneous and non-homogeneous periodic solutions through all parameters of the system which are spati...

Stability and Hopf bifurcation for Kaldor-Kalecki model of business cycles with two time delays

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...

Center manifold analysis and Hopf bifurcation of within-host virus model

A mathematical model of a within-host viral infection is presented. A local stability analysis of the model is conducted in two ways. At first, the basic reproduction number of the system is calculated. It is shown that when the reproduction number falls below unity, the disease free equilibrium (DFE) is globally asymptotically stable, and when it exceeds unity, the DFE is unstable and there ex...

Stability analysis of a noise-induced Hopf bifurcation

We study analytically and numerically the noise-induced transition between an absorbing and an oscillatory state in a Duffing oscillator subject to multiplicative, Gaussian white noise. We show in a non-perturbative manner that a stochastic bifurcation occurs when the Lyapunov exponent of the linearised system becomes positive. We deduce from a simple formula for the Lyapunov exponent the phase...