Related papers: On the relationship between equilibria and dynamic…
We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…
We introduce a model of randomly connected neural populations and study its dynamics by means of the dynamical mean-field theory and simulations. Our analysis uncovers a rich phase diagram, featuring high- and low-dimensional chaotic…
Disorder and noise in physical systems often disrupt spatial and temporal regularity, yet chaotic systems reveal how order can emerge from unpredictable behavior. Complex networks, spatial analogs of chaos, exhibit disordered, non-Euclidean…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
Simple binary-state coordination models are widely used to study collective socio-economic phenomena such as the spread of innovations or the adoption of products on social networks. The common trait of these systems is the occurrence of…
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…
Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical…
Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…
The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the…
How do networks of relationships evolve over time? We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite continuous shifts in individual relationships, the macroscopic structural properties of the…
Random neural networks are dynamical descriptions of randomly interconnected neural units. These show a phase transition to chaos as a disorder parameter is increased. The microscopic mechanisms underlying this phase transition are unknown,…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
Networks of the brain are composed of a very large number of neurons connected through a random graph and interacting after random delays that both depend on the anatomical distance between cells. In order to comprehend the role of these…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
Collective stable chaos consists of the persistence of disordered patterns in dynamical spatiotemporal systems possessing a negative maximum Lyapunov exponent. We analyze the role of the topology of connectivity on the emergence and…
Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics…
The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system…
A network of coupled time-varying systems, where individual nodes are interconnected through links, is a modeling framework widely used by many disciplines. For identical nodes displaying a complex behavior known as chaos, clusters of nodes…
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…
In a manner similar to the molecular chaos that underlies the stable thermodynamics of gases, neuronal system may exhibit microscopic instability in individual neuronal dynamics while a macroscopic order of the entire population possibly…