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The logistic equation has many applications and is used frequently in different fields, such as biology, medicine, and economics. In this paper, we study the stability of a single-species logistic model with a general distribution delay…

Dynamical Systems · Mathematics 2023-10-12 Isam Al-Darabsah

In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…

Dynamical Systems · Mathematics 2024-05-28 Javad A. Asadzade , Nazim I. Mahmudov

Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…

Adaptation and Self-Organizing Systems · Physics 2023-03-08 Philipp C. Böttcher , Benjamin Schäfer , Stefan Kettemann , Carsten Agert , Dirk Witthaut

Sufficient condition for the stability of a fractional order semi-linear system with multi-time delay is proposed.

Analysis of PDEs · Mathematics 2014-09-16 Supriyo Dutta , N. Sukavanam

The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…

Dynamical Systems · Mathematics 2008-03-27 M. De la Sen

Logistic functions are good models of biological population growth. They are also popular in marketing in modelling demand-supply curves and in a different context, to chart the sales of new products over time. Delays being inherent in any…

Populations and Evolution · Quantitative Biology 2012-11-30 Milind M. Rao , K. L. Preetish

In this paper we analyze a coupled system between a transport equation and an ordinary differential equation with time delay (which is a simplified version of a model for kidney blood flow control). Through a careful spectral analysis we…

Analysis of PDEs · Mathematics 2020-07-20 Serge Nicaise , Alessandro Paolucci , Cristina Pignotti

Stability analysis is performed for a linear differential equation with two delays. Geometric arguments show that when the two delays are rationally dependent, then the region of stability increases. When the ratio has the form 1/n, this…

Dynamical Systems · Mathematics 2013-08-08 Joseph M. Mahaffy , Timothy C. Busken

For the nonlinear second order Lienard-type equations with time-varying delays $$ \ddot{x}(t)+\sum_{k=1}^m f_k(t,x(t),\dot{x}(g_k(t)))+\sum_{k=1}^l s_k(t,x(h_k(t)))=0, $$ global asymptotic stability conditions are obtained. The results are…

Dynamical Systems · Mathematics 2016-06-13 Leonid Berezansky , Elena Braverman , Lev Idels

Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…

Dynamical Systems · Mathematics 2025-02-12 Prashant M. Gade , Sachin Bhalekar , Janardhan Chevala

We investigate the structure of the set of $T$-periodic solutions to periodically perturbed coupled delay differential equations on differentiable manifolds. By using fixed point index and degree-theoretic methods we prove the existence of…

Classical Analysis and ODEs · Mathematics 2014-11-19 Luca Bisconti , Marco Spadini

We study a mathematical model describing the dynamics of a pluripotent stem cell population involved in the blood production process in the bone marrow. This model is a differential equation with a time delay. The delay describes the cell…

Analysis of PDEs · Mathematics 2009-04-17 Mostafa Adimy , Fabien Crauste , Shigui Ruan

This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…

Dynamical Systems · Mathematics 2010-10-18 M. De La Sen

This article investigates the stability of pantograph delay differential equations, in which the delayed argument is proportional to the present time. We derive analytic criteria that partition the parameter plane into unstable,…

Dynamical Systems · Mathematics 2026-05-22 Sachin Bhalekar

We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion…

Dynamical Systems · Mathematics 2010-04-30 S. K. Bhowmik , D. B. Duncan , M. Grinfeld , G. J. Lord

We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…

Dynamical Systems · Mathematics 2023-06-13 Lucas Illing , Pierce Ryan , Andreas Amann

The purpose of this article is to introduce the original results which devoted with the nonlinear control system problems involves of nonlinear differential equations of fractional orders. Thus, this system is described with a mixed of…

Optimization and Control · Mathematics 2024-04-09 B. Hassoun , R. Al-Saphory , S. Hassan

The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we…

Analysis of PDEs · Mathematics 2025-07-04 Sofwah Ahmad , Szymon Cygan , Grzegorz Karch

We consider the stability of periodic map with period-$2$ in linear fractional difference equations where the function is $f(x)=ax$ at even times and $f(x)=bx$ at odd times. The stability of such a map for an integer order map depends on…

Dynamical Systems · Mathematics 2023-04-18 Sachin Bhalekar , Prashant M. Gade

In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…

Classical Analysis and ODEs · Mathematics 2020-02-17 H. T. Tuan , S. Siegmund