Related papers: Stability Boundaries in Second-order Time-delayed …
We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…
We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function,…
We study scalar delay equations $$\dot{x} (t) = \lambda f(x(t-1)) + b^{-1} (x(t) + x(t -p/2))$$ with odd nonlinearity $f$, real nonzero parameters $\lambda, \, b$, and two positive time delays $1,\ p/2$. We assume supercritical…
We study the effect of external stochastic modulation on a system with O(2) symmetry that exhibits a Hopf or oscillatory instability in the absence of modulation. The study includes a random component in both the control parameter of the…
We study stability of so-called synchronous slowly oscillating periodic solutions (SOPSs) for a system of identical delay differential equations (DDEs) with linear decay and nonlinear delayed negative feedback that are coupled through their…
We study the effects of time delayed linear and nonlinear feedbacks on the dynamics of a single Hopf bifurcation oscillator. Our numerical and analytic investigations reveal a host of complex temporal phenomena such as phase slips,…
We investigate the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics. Using a master stability…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…
We present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple model consisting of just two oscillators with a time delayed coupling, the bifurcation…
We give a sufficient condition for exponential stability of a network of lossless telegrapher's equations, coupled by linear time-varying boundary conditions. The sufficient conditions is in terms of dissipativity of the couplings, which is…
We prove that that second-order (double-loop) chaotic sigma-delta schemes are stable - within a certain parameter range, all state variables of the system are guaranteed to remain uniformly bounded. To our knowledge this is the first…
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…
Hopf bifurcation in networks of coupled ODEs creates periodic states in which the relative phases of nodes are well defined near bifurcation. When the network is a fully inhomogeneous nearest-neighbour coupled unidirectional ring, and node…
We analyze the asymptotic stability of a nonlinear system of two differential equations with delay describing the dynamics of blood cell production. This process takes place in the bone marrow where stem cells differentiate throughout…
We study the emergence of symmetric oscillatory behavior in multi-agent systems where each agent incorporates a continuous memory of its past states and past rates of change, modeled by distributed retarded and neutral delays. The…
We conduct a local stability and Hopf bifurcation analysis for Compound TCP, with small Drop-tail buffers, in three topologies. The first topology consists of two sets of TCP flows having different round trip times, and feeding into a core…
In this paper, we investigate synchronization of coupled second-order linear harmonic oscillators with random noises and time delays. The interaction topology is modeled by a weighted directed graph and the weights are perturbed by white…