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The existence of inter-dependence between multiple networks imparts an additional scale of complexity to such systems often referred to as `network of networks' (NON). We have investigated the robustness of NONs to random breakdown of their…
Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…
Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$…
Supplementing a lattice with long-range connections effectively models small-world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain. If the links have a wiring cost…
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…
Random Boolean networks have been used widely to explore aspects of gene regulatory networks. A modified form of the model through which to systematically explore the effects of increasing the number of gene states has previously been…
We study the problem of computing a minimal subset of nodes of a given asynchronous Boolean network that need to be controlled to drive its dynamics from an initial steady state (or attractor) to a target steady state. Due to the phenomenon…
We study the dynamical behaviour of the collective field of chaotic systems on small world lattices. Coupled neuronal systems as well as coupled logistic maps are investigated. We observe that significant changes in dynamical properties…
We propose a simple growing model for the evolution of small-world networks. It is introduced as a modified BA model in which all the edges connected to the new nodes are made locally to the creator and its nearest neighbors. It is found…
We study the dynamics of an epidemic-like model for the spread of a rumor on a small-world network. It has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of the network…
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…
In an increasingly connected world, the resilience of networked dynamical systems is important in the fields of ecology, economics, critical infrastructures, and organizational behaviour. Whilst we understand small-scale resilience well,…
Boolean networks serve as discrete models of regulation and signaling in biological cells. Identifying the key controllers of such processes is important for understanding the dynamical systems and planning further analysis. Here we…
Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…
Standard Random Boolean Networks display an order-disorder phase transition. We add to the standard Random Boolean Networks a disconnection rule which couples the control and order parameters. By this way, the system is driven to the…
The way in which different types of dynamics unfold in complex networks is intrinsically related to the propagation of activation along nodes, which is strongly affected by the network connectivity. In this work we investigate to which…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
We present analytic and numeric results for percolation in a network formed of interdependent spatially embedded networks. We show results for a treelike and a random regular network of networks each with $(i)$ unconstrained interdependent…
In this article, we design the distributed pinning controllers to globally stabilize a Boolean network (BN), specially a sparsely connected large-scale one, towards a preassigned subset of state space through the node-to-node message…
Boolean Networks and their dynamics are of great interest as abstract modeling schemes in various disciplines, ranging from biology to computer science. Whereas parallel update schemes have been studied extensively in past years, the level…