Related papers: Is there switching without suspended horseshoes?
We describe the dynamics of a simple adaptive network. The network architecture evolves to a number of disconnected components on which the dynamics is characterized by the possibility of differently synchronized nodes within the same…
This paper studies switching stabilization problems for continuous-time switched linear systems. We consider four types of switching stabilizability defined under different assumptions on the switching control input. The most general…
We investigate dynamical systems characterized by a time series of distinct semi-stable activity patterns, as they are observed in cortical neural activity patterns. We propose and discuss a general mechanism allowing for an adiabatic…
In this paper we investigate equilibria of continuous differential equation models of network dynamics. The motivation comes from gene regulatory networks where each directed edge represents either down- or up-regulation, and is modeled by…
In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
This paper investigates contraction properties of switched dynamical systems for the case that all modes are non-contracting, thereby extending existing results that require at least one mode to be contracting. Leveraging the property that…
This work is devoted to the study of global connections between typical generic singularities, named $T$-singularities, in piecewise smooth dynamical systems. Such a singularity presents the so-called nonsmooth diabolo, which consists on a…
We consider a Markov chain on $R^+$ with asymptotically zero drift and finite second moments of jumps which is positive recurrent. A power-like asymptotic behaviour of the invariant tail distribution is proven; such a heavy-tailed invariant…
We give an example of a transient reversible Markov chain that almost surely has only a finite number of cutpoints. We explain how this is relevant to a conjecture of Diaconis and Freedman and a question of Kaimanovich. We also answer…
Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in…
Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…
We prove that for every discrete-time linear switching system in two complex variables and with finitely many switching states, either the system is Lyapunov stable or there exists a trajectory which escapes to infinity with at least linear…
We have previously demonstrated that a switched affine system is stabilisable independently of the initial condition, i.e. there exists an asymptotically stabilising switching function which is the same for all initial conditions, if and…
There are few explicit examples in the literature of vector fields exhibiting complex dynamics that may be proved analytically. We construct explicitly a {two parameter family of vector fields} on the three-dimensional sphere $\EU^3$, whose…
The dynamics of cascading failures in spatial interdependent networks significantly depend on the interaction range of dependency couplings between layers. In particular, for increasing range of dependency couplings, different types of…
Network topologies can be non-trivial, due to the complex underlying behaviors that form them. While past research has shown that some processes on networks may be characterized by low-order statistics describing nodes and their neighbors,…
We prove an invariance principle for the bridge of a random walk conditioned to stay positive, when the random walk is in the domain of attraction of a stable law, both in the discrete and in the absolutely continuous setting. This includes…
We consider continuous time Hopfield-like recurrent networks as dynamical models for gene regulation and neural networks. We are interested in networks that contain n high-degree nodes preferably connected to a large number of Ns weakly…
Queueing networks are notoriously difficult to analyze sans both Markovian and stationarity assumptions. Much of the theoretical contribution towards performance analysis of time-inhomogeneous single class queueing networks has focused on…