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New Computational Tools for Modeling Chronic Myelogenous Leukemia

M. M. Peet, P. S. Kim, S.-I. Niculescu, D. Levy (2009)

Mathematical Modelling of Natural Phenomena

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 existence results of anti-periodic solutions of nonlinear impulsive functional differential equations

Yuji Liu, Xingyuan Liu (2013)

Mathematica Bohemica

This paper is a continuation of Y. Liu, Anti-periodic solutions of nonlinear first order impulsive functional differential equations, Math. Slovaca 62 (2012), 695–720. By using Schaefer's fixed point theorem, new existence results on anti-periodic solutions of a class of nonlinear impulsive functional differential equations are established. The techniques to get the priori estimates of the possible solutions of the mentioned equations are different from those used in known papers. An example is...

New interval oscillation criteria for second-order functional differential equations with nonlinear damping

Süleyman Öǧrekçi (2015)

Open Mathematics

This paper concerns the oscillation problem of second-order nonlinear damped ODE with functional terms.We give some new interval oscillation criteria which is not only based on constructing a lower solution of a Riccati type equation but also based on constructing an upper solution for corresponding Riccati type equation. We use a recently developed pointwise comparison principle between those lower and upper solutions to obtain our results. Some illustrative examples are also provided to demonstrate...

New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

Robert Hakl, Alexander Lomtatidze, Bedřich Půža (2002)

Mathematica Bohemica

The nonimprovable sufficient conditions for the unique solvability of the problem u ' ( t ) = ℓ ( u ) ( t ) + q ( t ) , u ( a ) = c , where ℓ C ( I ; ℝ ) → L ( I ; ℝ ) is a linear bounded operator, q ∈ L ( I ; ℝ ) , c ∈ ℝ , are established which are different from the previous results. More precisely, they are interesting especially in the case where the operator ℓ is not of Volterra’s type with respect to the point a .

New oscillation criteria for first order nonlinear delay differential equations

Xianhua Tang, Jianhua Shen (2000)

Colloquium Mathematicae

New oscillation criteria are obtained for all solutions of a class of first order nonlinear delay differential equations. Our results extend and improve the results recently obtained by Li and Kuang [7]. Some examples are given to demonstrate the advantage of our results over those in [7].

New qualitative methods for stability of delay systems

Erik I. Verriest (2001)

Kybernetika

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

Bingwen Liu (2015)

Annales Polonici Mathematici

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

Mimia Benhadri, Tomás Caraballo (2022)

Mathematica Bohemica

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.

Noise Shaping in Neural Populations with Global Delayed Feedback

O. Ávila Åkerberg, M. J. Chacron (2010)

Mathematical Modelling of Natural Phenomena

The interplay between intrinsic and network dynamics has been the focus of many investigations. Here we use a combination of theoretical and numerical approaches to study the effects of delayed global feedback on the information transmission properties of neural networks. Specifically, we compare networks of neurons that display intrinsic interspike interval correlations (nonrenewal) to networks that do not (renewal). We find that excitatory and...

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