Dynamical analysis of a delayed predator-prey system with birth pulse and impulsive harvesting at different moments.
Dynamics of delayed piecewise linear systems.
Dynamics of the tumor-immune system competition - the effect of time delay
The model analyzed in this paper is based on the model set forth by V.A. Kuznetsov and M.A. Taylor, which describes a competition between the tumor and immune cells. Kuznetsov and Taylor assumed that tumor-immune interactions can be described by a Michaelis-Menten function. In the present paper a simplified version of the Kuznetsov-Taylor model (where immune reactions are described by a bilinear term) is studied. On the other hand, the effect of time delay is taken into account in order to achieve...
Existence and exponential stability of positive almost periodic solutions for a model of hematopoiesis.
Existence and global attractivity of positive periodic solutions for a delayed competitive system with the effect of toxic substances and impulses
In this paper, a class of non-autonomous delayed competitive systems with the effect of toxic substances and impulses is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantees the existence of at least one positive periodic solution, and by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are established.
Existence and stability of periodic solutions for a class of generalized nonautonomous neural networks with distributed delays.
Existence and stability of solutions for nonlinear Mecking-Lucke-Grilhe equations.
Existence and uniqueness of a positive steady state solution for a logistic system of differential difference equations.
Existence and uniqueness of positive periodic solutions of delayed Nicholson's blowflies models
This paper is concerned with a class of Nicholson's blowflies models with multiple time-varying delays. By applying the coincidence degree, some criteria are established for the existence and uniqueness of positive periodic solutions of the model. Moreover, a totally new approach to proving the uniqueness of positive periodic solutions is proposed. In particular, an example is employed to illustrate the main results.
Existence of periodic solutions for a delayed ratio-dependent three-species predator-prey diffusion system on time scales.
Existence of periodic solutions of a delayed predator-prey system on time scales.
Gene regulatory networks and delay differential equations.
Generalization of the Kermack-McKendrick SIR Model to a Patchy Environment for a Disease with Latency
In this paper, with the assumptions that an infectious disease has a fixed latent period in a population and the latent individuals of the population may disperse, we reformulate an SIR model for the population living in two patches (cities, towns, or countries etc.), which is a generalization of the classic Kermack-McKendrick SIR model. The model is given by a system of delay differential equations with a fixed delay accounting for the latency and non-local terms caused by the mobility of the...
Global behaviors of a chemostat model with delayed nutrient recycling and periodically pulsed input.
Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections
We describe the global dynamics of a disease transmission model between two regions which are connected via bidirectional or unidirectional transportation, where infection occurs during the travel as well as within the regions. We define the regional reproduction numbers and the basic reproduction number by constructing a next generation matrix. If the two regions are connected via bidirectional transportation, the basic reproduction number characterizes the existence of equilibria as well as...
Global stability for a delayed predator-prey system with stage structure for the predator.
Global stability, periodic solutions, and optimal control in a nonlinear differential delay model.
Harmless delays in a discrete ratio-dependent periodic predator-prey system.
Hopf bifurcation for simple food chain model with delay.
Influence of time delays on the Hahnfeldt et al. angiogenesis model dynamics
We study the influence of time delays on the dynamics of the general Hahnfeldt et al. model of an angiogenesis process. We analyse the dynamics of the system for different values of the parameter α which reflects the strength of stimulation of the vessel formation process. Time delays are introduced in three subprocesses: tumour growth, stimulation and inhibition of vessel formation (represented by endothelial cell dynamics). We focus on possible destabilisation of the positive steady state due...