Global stability of polytopic linear time-varying dynamic systems under time-varying point delays and impulsive controls.
Global stability of sets for impulsive differential-difference equations by Lyapunov's direct method
Global stability, periodic solutions, and optimal control in a nonlinear differential delay model.
Harvesting control for a stage-structured predator-prey model with Ivlev's functional response and impulsive stocking on prey.
Immunological barrier for infectious diseases
A nonlinear mathematical model with distributed delay is proposed to describe the reaction of a human organism to a pathogen agent. The stability of the disease free state is analyzed, showing that there exists a large set of initial conditions in the attraction basin of the disease-free state whose border is defined as the immunological barrier.
Impulse control in Kalman-like filtering problems.
Impulsive exponential stabilization of functional differential systems with infinite delay.
Impulsive stabilization of cellular neural networks with time delay via Lyapunov functionals.
Impulsive stabilization of high-order nonlinear retarded differential equations
In this paper, impulsive stabilization of high-order nonlinear retarded differential equations is investigated by using Lyapunov functions and some analysis methods. Our results show that several non-impulsive unstable systems can be stabilized by imposition of impulsive controls. Some recent results are extended and improved. An example is given to demonstrate the effectiveness of the proposed control and stabilization methods.
Indecision in Neural Decision Making Models
Computational models for human decision making are typically based on the properties of bistable dynamical systems where each attractor represents a different decision. A limitation of these models is that they do not readily account for the fragilities of human decision making, such as “choking under pressure”, indecisiveness and the role of past experiences on current decision making. Here we examine the dynamics of a model of two interacting neural populations with mutual time–delayed inhibition....
Inequalities for solutions of systems with “pure” 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...
Initial value problems for nonlinear nonresonant delay differential equations with possibly infinite delay.
Integral manifold of the parabolic differential equation with deviating argument
Involutions of real intervals
This paper shows a simple construction of continuous involutions of real intervals in terms of continuous even functions. We also study smooth involutions defined by symmetric equations. Finally, we review some applications, in particular a characterization of isochronous potentials by means of smooth involutions.
perturbations in delay differential equations.
Liapunov-type inequality for delay-differential equations of third order
A Liapunov-type inequality for a class of third order delay-differential equations is derived.
Linear and structural stability of a cell division process model.
Local center manifold for parabolic equations with infinite delay
The existence and attractivity of a local center manifold for fully nonlinear parabolic equation with infinite delay is proved with help of a solutions semigroup constructed on the space of initial conditions. The result is applied to the stability problem for a parabolic integrodifferential equation.
Lyapunov-Razumikhin method for asymptotic stability of sets for impulsive functional differential equations.