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This paper addresses analytical aspects of deterministic, continuous-time dynamical systems defined on networks. The goal is to model and analyze certain phenomena which must be framed beyond the context of networked dynamical systems,…

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…

Plasticity-led evolution is a form of evolution where a change in the environment induces novel traits via phenotypic plasticity, after which the novel traits are genetically accommodated over generations under the novel environment. This…

Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce…

Diverse biological networks exhibit universal features distinguished from those of random networks, calling much attention to their origins and implications. Here we propose a minimal evolution model of Boolean regulatory networks, which…

Living organisms must respond to environmental changes. Generally, accurate and rapid responses are provided by simple, unidirectional networks that connect inputs with outputs. Besides accuracy and speed, biological responses should also…

Robustness to mutations and noise has been shown to evolve through stabilizing selection for optimal phenotypes in model gene regulatory networks. The ability to evolve robust mutants is known to depend on the network architecture. How do…

The interplay between topology and dynamics in complex networks is a fundamental but widely unexplored problem. Here, we study this phenomenon on a prototype model in which the network is shaped by a dynamical variable. We couple the…

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node…

Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…

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…

Networks are widely used to model the interaction between individual dynamical systems. In many instances, the total number of units as well as the interaction coupling are not fixed in time, but rather constantly evolve. In terms of…

Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…

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…

Genetic regulatory networks with adaptive responses are widely studied in biology. Usually, models consisting only of a few nodes have been considered. They present one input receptor for activation and one output node where the adaptive…

Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…

Genetic regulatory networks enable cells to respond to the changes in internal and external conditions by dynamically coordinating their gene expression profiles. Our ability to make quantitative measurements in these biochemical circuits…

One of the hallmarks of real networks is their ability to perform increasingly complex tasks as their topology evolves. To explain this, it has been observed that as a network grows certain subsets of the network begin to specialize the…

We present a model for the description of the evolution of contacts among individuals in a network. At each time step each individual is associated with a domain or neighborhood of fully connected agents.The dynamics of this changing…

Here we provide a detailed analysis, along with some extensions and additonal investigations, of a recently proposed self-organised model for the evolution of complex networks. Vertices of the network are characterised by a fitness variable…