Related papers: Chaotic behavior in diffusively coupled systems
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…
We present and analyze a topologically induced transition from ordered, synchronized to disordered dynamics in directed networks of oscillators. The analysis reveals where in the space of networks this transition occurs and its underlying…
We discuss, in this paper, the dynamical properties of extremely diluted, non-monotonic neural networks. Assuming parallel updating and the Hebb prescription for the synaptic connections, a flow equation for the macroscopic overlap is…
For infinitely large sparse networks of spiking neurons mean field theory shows that a balanced state of highly irregular activity arises under various conditions. Here we analytically investigate the microscopic irregular dynamics in…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
In this paper we study the asymptotic behavior of solutions to systems of strongly coupled integral equations with oscillatory coefficients. The system of equations is motivated by a peridynamic model of the deformation of heterogeneous…
The multiplicity of routes from deterministic chaos to turbulence caused by the spontaneous breaking of the local reflectional symmetry in the flows induced by Rayleigh-Taylor instability has been studied using the notion of distributed…
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
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…
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…
Neuromorphic networks can be described in terms of coarse-grained variables, where emergent sustained behaviours spontaneously arise if stochasticity is properly taken in account. For example it has been recently found that a directed…
Resilience is a system's ability to maintain its function when perturbations and errors occur. Whilst we understand low-dimensional networked systems' behavior well, our understanding of systems consisting of a large number of components is…
We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. We assume…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
The erratic nature of chaotic behavior is thought to erode the stability of periodic behavior, including topological oscillations. However, we discover that in the presence of chaos, non-trivial topology not only endures but also provides…
Many real world networks are characterized by adaptive changes in their topology depending on the dynamic state of their nodes. Here we study epidemic dynamics in an adaptive network, where susceptibles are able to avoid contact with…
We consider here a recently proposed geometrical criterion for local instability based on the geodesic deviation equation. Although such a criterion can be useful in some cases, we show here that, in general, it is neither necessary nor…
We demonstrate that solitary states can be widely observed for networks of coupled oscillators with local, non-local and global couplings, and they preserve in both thermodynamic and Hamiltonian limits. We show that depending on units' and…
Given a reaction-diffusion system interacting via a complex network, we propose two different techniques to modify the network topology while preserving its dynamical behaviour. In the region of parameters where the homogeneous solution…
Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently…