Related papers: Phase transition in a class of non-linear random n…
We numerically investigate jamming transitions in complex heterogeneous networks. Inspired by Internet routing protocols, we study a general model that incorporates local traffic information through a tunable parameter. The results show…
The notion of (auto) catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems. Here we study…
We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The…
The dynamics of nonlocally coupled dissipative kicked rotors is rich and complex. In this study, we consider a network of rotors where each interacts equally with a certain range of its neighbors. We focus on the influence of the coupling…
We describe non-equilibrium phase transitions in arrays of dynamical systems with cubic nonlinearity driven by multiplicative Gaussian white noise. Depending on the sign of the spatial coupling we observe transitions to ferromagnetic or…
In this paper we study the dynamics of nonlinear random walks. While typical random walks on networks consist of standard Markov chains whose static transition probabilities dictate the flow of random walkers through the network, nonlinear…
In order to investigate the role of the weight in weighted networks, the collective behavior of the Ising system on weighted regular networks is studied by numerical simulation. In our model, the coupling strength between spins is inversely…
While criticality is widely observed in neural networks, its underlying neural mechanism is not known well. We consider a network of $N$ excitatory leaky integrated and fire (LIF) neurons that reside on a regular lattice with periodic…
Most models of complex systems have been homogeneous, i.e., all elements have the same properties (spatial, temporal, structural, functional). However, most natural systems are heterogeneous: few elements are more relevant, larger,…
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their…
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
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…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
Recently, De Martino et al have presented a general framework for the study of transportation phenomena on complex networks. One of their most significant achievements was a deeper understanding of the phase transition from the uncongested…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
The complex dynamics of gene expression in living cells can be well-approximated using Boolean networks. The average sensitivity is a natural measure of stability in these systems: values below one indicate typically stable dynamics…
It has been proposed that adaptation in complex systems is optimized at the critical boundary between ordered and disordered dynamical regimes. Here, we review models of evolving dynamical networks that lead to self-organization of network…
We investigate the role of the spectral dimension $d_s$ in determining the universality of phase transitions on a complex network. Due to its structural heterogeneity, a complex network generally acts as a disordered system. Specifically,…
We analyze the synchronization transition for a pair of coupled identical Kauffman networks in the chaotic phase. The annealed model for Kauffman networks shows that synchronization appears through a transcritical bifurcation, and provides…