Harmless delays in a discrete ratio-dependent periodic predator-prey system.
Harvesting control for a stage-structured predator-prey model with Ivlev's functional response and impulsive stocking on prey.
Harvesting of a single-species system incorporating stage structure and toxicity.
Herbivore harvesting and alternative steady states in coral reefs
Coral reefs can undergo relatively rapid changes in the dominant biota, a phenomenon referred to as phase shift. Degradation of coral reefs is often associated with changes in community structure towards a macroalgae-dominated reef ecosystem due to the reduction in herbivory caused by overfishing. We investigate the coral-macroalgal phase shift due to the effects of harvesting of herbivorous reef fish by means of a continuous time model in the food chain. Conditions for local asymptotic stability...
Hierarchically interacting Fleming-Viot processes with selection and mutation: Multiple space time scale analysis and quasi-equilibria.
Homoclinic orbits in a two-patch predator-prey model with Preisach hysteresis operator
Systems of operator-differential equations with hysteresis operators can have unstable equilibrium points with an open basin of attraction. Such equilibria can have homoclinic orbits attached to them, and these orbits are robust. In this paper a population dynamics model with hysteretic response of the prey to variations of the predator is introduced. In this model the prey moves between two patches, and the derivative of the Preisach operator is used to describe the hysteretic flow between the...
Homogeneous Systems with a Quiescent Phase
Recently the effect of a quiescent phase (or dormant/resting phase in applications) on the dynamics of a system of differential equations has been investigated, in particular with respect to stability properties of stationary points. It has been shown that there is a general phenomenon of stabilization against oscillations which can be cast in rigorous form. Here we investigate, for homogeneous systems, the effect of a quiescent phase, and more generally, a phase with slower dynamics. We show that...
Hopf Bifurcation Analysis of Pathogen-Immune Interaction Dynamics With Delay Kernel
The aim of this paper is to study the steady states of the mathematical models with delay kernels which describe pathogen-immune dynamics of infectious diseases. In the study of mathematical models of infectious diseases it is important to predict whether the infection disappears or the pathogens persist. The delay kernel is described by the memory function that reflects the influence of the past density of pathogen in the blood and it is given by a nonnegative bounded and normated function k defined...
Hopf bifurcation for a model of HIV infection of T cells with virus released delay.
Hopf bifurcation for simple food chain model with delay.
Hybrid matrix models and their population dynamic consequences
In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation as well...
Hybrid matrix models and their population dynamic consequences
In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation as...
Hybrid Taguchi-differential evolution algorithm for parameter estimation of differential equation models with application to HIV dynamics.