相关论文: Analysis of a Class of Two-delay Fractional Differ…

This manuscript deals with the stability and bifurcation analysis of the equation $D^{2\alpha}x(t)+c D^{\alpha}x(t)=a x(t)+b x(t-\tau)$, where $0<\alpha<1$ and $\tau>0$. We sketch the boundaries of various stability regions in the parameter…

This paper investigates the stability of different regions in the $(k,\gamma)$-plane for a class of fractional delay differential equations given by \begin{equation} D^{\alpha} x(t) = -\gamma x(t) + g\big(x(t - \tau_1)\big) - e^{-\gamma…

Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…

This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…

We consider the linear equation including two fractional order difference operators, viz. $\Delta^{\alpha}$ and $\Delta^{\beta}$, $0<\beta<\alpha \leq 1$. The sequence representation will be provided to find the solution in an easier way.…

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…

Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear…

Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…

The sunflower equation describes the motion of the tip of a plant due to the auxin transportation under the influence of gravity. This work proposes the fractional-order generalization to this delay differential equation. The equation…

Analysis of the systems involving delay is a popular topic among applied scientists. In the present work, we analyze the generalized equation $D^{\alpha} x(t) = g\left(x(t-\tau_1), x(t-\tau_2)\right)$ involving two delays viz. $\tau_1\geq…

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…

For the fractional order systems \[D^\alpha x(t)=f(x),\quad 0<\alpha\leq 1,\] one can have a critical value of $\alpha$ viz $\alpha_*$ such that the system is stable for $0<\alpha<\alpha_*$ and unstable for $\alpha_*<\alpha\leq 1$. In…

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…

We consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial solution which are independent of the distributions. For the…

We study the two state model which describes the balance equation for carbon dioxide and oxygen. These are nonlinear parameter dependent and because of the transport delay in the respiratory control system, they are modeled with delay…

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…

We consider the scalar delay differential equation $$ \dot{x}(t)=-x(t)+f_{K}(x(t-1)) $$ with a nondecreasing feedback function $f_{K}$ depending on a parameter $K$, and we verify that a saddle-node bifurcation of periodic orbits takes place…

This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.

We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with quadratic term and delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try…