Related papers: Global stability in the Ricker model with delay an…
For a class of $(N+1)$-dimensional systems of differential delay equations with a cyclic and monotone negative feedback structure, we construct a two-dimensional invariant manifold, on which phase curves spiral outward towards a bounding…
Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…
In this paper, we consider the Kirchhoff plate equation with delay terms on the boundary control are added (see system \eqref{p5-2.1} below). we give some instability examples of system \eqref{p5-2.1} for some choices of delays. Finally, we…
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…
In this paper, we consider the dynamics of a delayed reaction-diffusion mussel-algae system subject to Neumann boundary conditions. When the delay is zero, we show the existence of positive solutions and the global stability of the boundary…
This paper is concerned with the global stability of non-critical/critical traveling waves with oscillations for time-delayed nonlocal dispersion equations. We first theoretically prove that all traveling waves, especially the critical…
This paper investigates the dynamical behavior of periodic solutions for a class of second-order non-autonomous differential equations. First, based on the Lyapunov-Schmidt reduction method for finite-dimensional functions, the…
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…
We explore stability and instability of rapidly oscillating solutions $x(t)$ for the hard spring delayed Duffing oscillator $$x''(t)+ ax(t)+bx(t-T)+x^3(t)=0.$$ Fix $T>0$. We target periodic solutions $x_n(t)$ of small minimal periods…
We investigate stability properties of a type of periodic solutions of the $N$-vortex problem on general domains $\Omega\subset \mathbb{R}^2$. The solutions in question bifurcate from rigidly rotating configurations of the whole-plane…
We study the dynamics of a discrete phytoplankton-zooplankton model with Holling type~II grazing and Holling type~III toxin release. The existence and stability of positive fixed points are analyzed, and conditions for the occurrence of…
We study the periodic solutions of the delay equation $\dot{x}(t)=f(x(t),x(t-1))$, where $f$ scalar is strictly monotone in the delayed component and has even-odd symmetry. We completely describe the global bifurcation structure of periodic…
In this paper we study global nonlinear stability for the Dirac-Klein-Gordon system in two and three space dimensions for small and regular initial data. In the case of two space dimensions, we consider the Dirac-Klein-Gordon system with a…
Simultaneous stabilization problem arises in various systems and control applications. This paper introduces a new approach to addressing this problem in the multivariable scenario, building upon our previous findings in the scalar case.…
Nonlinear normal modes are periodic orbits that survive in nonlinear many-body Hamiltonian systems, and their instability is crucial for relaxation dynamics. Here, we study the instability process of the $\pi/3$-mode in the…
We study stable allocations in an exchange economy with indivisible goods. The problem is well-known to be challenging, and rich enough to encode fundamentally unstable economies, such as the roommate problem. Our approach stems from…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
Vickrey's classic single-bottleneck departure time choice equilibrium model exhibits instability under many plausible day-to-day learning dynamics. Such instability is not observed in reality -- does this difference stem from the day-to-day…
This document proves global boundedness and decay for axisymmetric perturbations of a known solution to the wave map problem from a slowly rotating $|a|\ll M$ Kerr spacetime to the hyperbolic plane. This problem is motivated by the general…
It is well-known that wave-type equations with memory, under appropriate assumptions on the memory kernel, are uniformly exponentially stable. On the other hand, time delay effects may destroy this behavior. Here, we consider the…