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We investigate how the dimensionality of the embedding space affects the microscopic crackling dynamics and the macroscopic response of heterogeneous materials. Using a fiber bundle model with localized load sharing computer simulations are…
Attacks on networks is a very important issue in developing strategies of eradicating spreads of malicious phenomena in networks, such as epidemics and fake information, which are generally named in the research networks immunization. The…
We consider the Bak-Tang-Wiesenfeld (BTW) and the Manna sandpile models of self-organized criticality. In the models, previous studies revealed a signature of long-range temporal correlations in the avalanche activity. We examine the power…
Fiber bundles with statistically distributed thresholds for breakdown of individual fibers are interesting models of the static and dynamics of failures in materials under stress. They can be analyzed to an extent that is not possible for…
Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in…
We introduce a general framework for models of cascade and contagion processes on networks, to identify their commonalities and differences. In particular, models of social and financial cascades, as well as the fiber bundle model, the…
Connectivity is one of the most fundamental properties of wireless multi-hop networks. A network is said to be connected if there is a path between any pair of nodes. A convenient way to study the connectivity of a random network is by…
Cascades arise in many contexts (e.g., neuronal avalanches, social contagions, and system failures). Despite evidence that propagations often involve higher-order dependencies, cascade theory has largely focused on models with…
Growing networks decorated with antiferromagnetically coupled spins are archetypal examples of complex systems due to the frustration and the multivalley character of their energy landscapes. Here we use the damage spreading method (DS) to…
Cascade models based on dynamical complex networks are proposed as models of turbulent energy cascade. Taking a simple shell model as the initial regular lattice with only nearest neighbor interactions, small world network models are…
Random Threshold Networks with sparse, asymmetric connections show complex dynamical behavior similar to Random Boolean Networks, with a transition from ordered to chaotic dynamics at a critical average connectivity $K_c$. In this type of…
Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However, the research is focused on systems with only one type of links, connectivity links. We review a recently…
Tipping points are critical thresholds of parameters where tiny perturbations can lead to abrupt and large qualitative changes in the systems. Many real-world systems that exhibit tipping behavior can be represented as networks of…
Much work has been devoted to studying percolation of networks and interdependent networks under varying levels of failures. Researchers have considered many different realistic network structures, but thus far no study has incorporated the…
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…
Complex systems are large collections of entities that organize themselves into non-trivial structures that can be represented by networks. A key emergent property of such systems is robustness against random failures or targeted attacks…
There is a commonality among contagious diseases, tweets, urban crimes, nuclear reactions, and neuronal firings that past events facilitate the future occurrence of events. The spread of events has been extensively studied such that the…
We introduce an external control to reduce the size of avalanches in some sandpile models exhibiting self organized criticality. This rather intuitive approach seems to be missing in the vast literature on such systems. The control action,…
We present the mathematical analysis of generalized complex contagions in clustered multiplex networks for susceptible-infected-recovered (SIR)-like dynamics. The model is intended to understand diffusion of influence, or any other…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…