Related papers: Stability Analysis of A Single-Species Model with …
Reaction delays are important in determining the qualitative dynamical properties of a platoon of vehicles traveling on a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of the Modified Optimal…
We investigate a diffusive, stage-structured epidemic model with the maturation delay and freely-moving delay. Choosing delays and diffusive rates as bifurcation parameters, the only possible way to destabilize the endemic equilibrium is…
Reaction delays play an important role in determining the qualitative dynamical properties of a platoon of vehicles traversing a straight road. In this paper, we investigate the impact of delayed feedback on the dynamics of the Classical…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases…
This paper investigates a class of reaction-diffusion population models defined on a bounded domain, characterized by a general time-delayed per capita growth rate and a general advection term. Notably, the growth rate encompasses both…
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…
We model intracellular regulatory dynamics with threshold-type state-dependent delay and investigate the effect of the state-dependent diffusion time. A general model which is an extension of the classic differential equation models with…
In this paper we investigate the impact of delayed tax revenues on the fiscal policy out-comes. Choosing the delay as a bifurcation parameter we study the direction and the stability of the bifurcating periodic solutions. With respect to…
We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns…
In this paper, we consider a continuous-time model with discrete and dis-tributed delays to describe how two pieces of information interact in online social networks. Sufficient conditions are carried out to illustrate the stability of each…
We investigate the scalar autonomous equation with two discrete delays $$ \dot{x}(t)=f(x(t),x(t-r),x(t-\sigma)), $$ where $f:\mathbb{R}^3\rightarrow \mathbb{R}$ is a continuously differentiable non-linear function such that $f(0,0,0)=0$. It…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
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…
The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation $D^\alpha x(t)=a…
This paper generalizes the existing minimal model of the hypothalamic-pituitary-adrenal (HPA) axis in a realistic way, by including memory terms: distributed time delays, on one hand and fractional-order derivatives, on the other hand. The…
In this paper, the dynamics of a modified Leslie-Gower predator-prey system with two delays and diffusion is considered. By calculating stability switching curves, the stability of positive equilibrium and the existence of Hopf bifurcation…
In this paper, we analyze some local stability and local bifurcation properties of the Proportionally fair, TCP fair, and the Delay-based dual algorithms in the presence of two distinct time delays. In particular, our focus is on the…
Various field and laboratory experiments show that prey refuge plays a significant role in the stability of prey-predator dynamics. On the other hand, theoretical studies show that delayed system exhibits a much more realistic dynamics than…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…