The goal of this paper is to establish the applicability of the Lyapunov-Schmidt reduction and the Centre Manifold Theorem for a class of hyperbolic partial differential equation models with nonlocal interaction terms describing the aggregation dynamics of animals/cells in a one-dimensional domain with periodic boundary conditions. We show the Fredholm property for the linear operator obtained ...

UMIST The use of boundary locus plots in the identiication of bifurcation points in numerical approximation of delay diierential equations Abstract We are interested in nonlinear delay diierential equations which have a Hopf bifurcation. We assume zero is a steady state for the problem, and so a Hopf bifurcation point lies on the boundary of the region of asymptotic stability for the zero solut...

UMIST The use of boundary locus plots in the identiication of bifurcation points in numerical approximation of delay diierential equations Abstract We are interested in nonlinear delay diierential equations which have a Hopf bifurcation. We assume zero is a steady state for the problem, and so a Hopf bifurcation point lies on the boundary of the region of asymptotic stability for the zero solut...

This paper is concerned with a delayed SIRS epidemic model with a nonlinear incidence rate. The main results are given in terms of local stability and Hopf bifurcation. Sufficient conditions for the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained by regarding the time delay as the bifurcation parameter. Further, the properties of Hopf bifurcation such ...

A subcritical Hopf bifurcation in a dynamical system modeled by a scalar nonlinear delay differential equation is studied theoretically and experimentally. The subcritical Hopf bifurcation leads to a significant domain of bistability where stable steady and time-periodic states coexist.

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...

We show that the perturbation theory for dual semigroups (sun-star-calculus) that has proved useful for analyzing delay-differential equations is equally efficient for dealing with Volterra functional equations. In particular, we obtain both the stability and instability parts of the principle of linearized stability and the Hopf bifurcation theorem. Our results apply to situations in which the...

Using spatial dynamics, we prove a Hopf bifurcation theorem for viscous Lax shocks in viscous conservation laws. The bifurcating viscous shocks are unique (up to time and space translation), exponentially localized in space, periodic in time, and their speed satisfies the Rankine–Hugoniot condition. We also prove an ”exchange of spectral stability” result for superand subcritical bifurcations, ...