Related papers: Fractional Order Sunflower Equation: Stability, Bi…
In aggregation-fragmentation processes, a steady state is usually reached in the long time limit. This indicates the existence of a fixed point in the underlying system of ordinary differential equations. The next simplest possibility is an…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by…
This paper considers linear functional equations on $\mathbb R^d$ with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential…
The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have real rational number values. Applicable characteristic…
Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
Fractional derivatives of Prabhakar type are capturing an increasing interest since their ability to describe anomalous relaxation phenomena (in dielectrics and other fields) showing a simultaneous nonlocal and nonlinear behaviour. In this…
Algorithms of control of differential equations solutions are under investigation in the article. Idealized and real modifications of the algorithms are distinguished. An equation, which can be the base equation for investigation of the…
Conventional grain growth is rate-limited by the mobility of grain boundary. To describe similar phenomena limited by the mobility of other grain junctions, we have developed a general theory allowing for size-dependent mobility and its…
This study presents a study of equilibrium points, periodic orbits, stabilities, and manifolds in a rotating plane symmetric potential field. It has been found that the dynamical behaviour near equilibrium points is completely determined by…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
A novel flow instability emerging during a rheometric flow of a phase change material sheared in the vicinity of the solid-fluid transition is reported. Right above the onset of the flow induced crystallisation, the presence of the crystals…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
Consider the general scalar balance law $\partial_t u + \Div f(t, x,u) = F(t,x,u)$ in several space dimensions. The aim of this note is to estimate the dependence of its solutions from the flow $f$ and from the source $F$. To this aim, a…
There is a close connection between stability and oscillation of delay differential equations. For the first-order equation $$ x^{\prime}(t)+c(t)x(\tau(t))=0,~~t\geq 0, $$ where $c$ is locally integrable of any sign, $\tau(t)\leq t$ is…
Empirical diagnosis of stability has received considerable attention, mostly focused on variance metrics for early warning signals of abrupt system change. Despite this, the theoretical foundation and application has been limited to…
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…
Classical conditions for asymptotic stability of periodic solutions bifurcating from a limit cycle rely on the derivative of the corresponding bifurcation function F at the bifurcation point t. We show that for analytic systems this result…
We study the emergence of periodic oscillations through a Hopf bifurcation in a scalar diffusion equation on the half line coupled to a dynamic boundary condition. Our results quantify the effect of delay through the buffering in the…