Neural networks with memory.
New Computational Tools for Modeling Chronic Myelogenous Leukemia
In this paper, we consider a system of nonlinear delay-differential equations (DDEs) which models the dynamics of the interaction between chronic myelogenous leukemia (CML), imatinib, and the anti-leukemia immune response. Because of the chaotic nature of the dynamics and the sparse nature of experimental data, we look for ways to use computation to analyze the model without employing direct numerical simulation. In particular, we develop several tools using Lyapunov-Krasovskii analysis that allow...
New criteria for exponential stability of linear neutral differential systems with distributed delays
We present new explicit criteria for exponential stability of general linear neutral time-varying differential systems. Particularly, our results give extensions of the well-known stability criteria reported in [3,11] to linear neutral time-varying differential systems with distributed delays.
New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations.
New qualitative methods for stability of delay systems
A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The generalization is here in using the comparison theorem directly with a different scalar equation with known...
New results on global exponential stability of almost periodic solutions for a delayed Nicholson blowflies model
This paper is concerned with a class of Nicholson's blowflies models with multiple time-varying delays, which is defined on the nonnegative function space. Under appropriate conditions, we establish some criteria to ensure that all solutions of this model converge globally exponentially to a positive almost periodic solution. Moreover, we give an example with numerical simulations to illustrate our main results.
New sufficient conditions for global asymptotic stability of a kind of nonlinear neutral differential equations
This paper addresses the stability study for nonlinear neutral differential equations. Thanks to a new technique based on the fixed point theory, we find some new sufficient conditions ensuring the global asymptotic stability of the solution. In this work we extend and improve some related results presented in recent works of literature. Two examples are exhibited to show the effectiveness and advantage of the results proved.
Nonautonomous differential equations of alternately retarded and advanced type.
Nonnegative point spectrum for differential equations with infinite delays
Nonnegativity of the Cauchy matrix and exponential stability of a neutral type system of functional differential equations.
Numerical stability test of neutral delay differential equations.