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This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
We consider three kinds of discrete-time arrival processes: transient, intermediate and recurrent, characterized by a finite, possibly finite and infinite number of events, respectively. In this context, we study renewal processes which are…
Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis.…
We present an analytical framework that allows the quantitative study of statistical dynamic properties of networks with adaptive nodes that have memory and is used to examine the emergence of oscillations in networks with response…
We consider unstable attractors; Milnor attractors $A$ such that, for some neighbourhood $U$ of $A$, almost all initial conditions leave $U$. Previous research strongly suggests that unstable attractors exist and even occur robustly (i.e.…
Order can spontaneously emerge from seemingly noisy interactions between biological agents, like a flock of birds changing their direction of flight in unison, without a leader or an external cue. We are interested in the generic conditions…
An adaptive network model using SIS epidemic propagation with link-type dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out,…
Emerging collective behavior in complex dynamical networks depends on both coupling function and underlying coupling topology. Through this perspective, we provide a brief yet profound excerpt of recent research efforts that explore how the…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
We investigate the combined effects of distributed delay and the balance between excitatory and inhibitory nodes on the stability of synchronous oscillations in a network of coupled Stuart--Landau oscillators. To this end a network model is…
We study numerically and analytically the quench dynamics of isolated many-body quantum systems. Using full random matrices from the Gaussian orthogonal ensemble, we obtain analytical expressions for the evolution of the survival…
We study the dynamics of the entanglement between two oscillators that are initially prepared in a general two-mode Gaussian state and evolve while coupled to the same environment. In a previous paper we showed that there are three…
We propose a new mechanism for pattern formation based on the global alternation of two dynamics neither of which exhibits patterns. When driven by either one of the separate dynamics, the system goes to a spatially homogeneous state…
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
Dense suspensions of self-propelled rod-like particles exhibit a fascinating variety of non-equilibrium phenomena. By means of computer simulations of a minimal model for rigid self-propelled colloidal rods with variable shape we explore…
The evolution of the entanglement between oscillators that interact with the same environment displays highly non-trivial behavior in the long time regime. When the oscillators only interact through the environment, three dynamical phases…
We investigate the modes of oscillation of heterogeneous ring-networks of quadratic integrate-and-fire neurons with non-local, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient…
Deterioration in the dynamical activities may come up naturally or due to environmental influences in a massive portion of biological and physical systems. Such dynamical degradation may have outright effect on the substantive network…
We study the collective dynamics of identical phase oscillators on globally coupled networks whose interactions are asymmetric and mediated by positive and negative couplings. We split the set of oscillators into two interconnected…
The effects of a distributed 'weak generic kernel' delay on cyclically coupled limit cycle and chaotic oscillators are considered. For coupled Van der Pol oscillators (and in fact, other oscillators as well) the delay can produce…