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This paper introduces a conception that any weighted directed network topology is almost decouplable, which can help to transform the topology into a similar form being composed of uncoupled vertices, and thus reduce the complexity of…
In this contribution we analyze the exponential stability of power networks modeled with the Telegrapher's equations as a system of balance laws on the edges. We show the equivalence of periodic solutions of these Telegrapher's equations…
We analyze the consequences of iterative measurement-induced nonlinearity on the dynamical behavior of qubits. We present a one-qubit scheme where the equation governing the time evolution is a complex-valued nonlinear map with one complex…
The structure of a complex network plays a crucial role in determining its dynamical properties. In this work, we show that the the degree to which a network is directed and hierarchically organised is closely associated with the degree to…
We show, using generic globally-coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting…
We consider delayed chemical reaction networks with generalized kinetics of product form and show that complex balancing implies that within each positive stoichiometric compatibility class there is a unique positive equilibrium that is…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
This paper presents a small-gain theorem for networks composed of a countably infinite number of finite-dimensional subsystems. Assuming that each subsystem is exponentially input-to-state stable, we show that if the gain operator,…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
Although most networks in nature exhibit complex topology the origins of such complexity remains unclear. We introduce a model of a growing network of interacting agents in which each new agent's membership to the network is determined by…
Evaluating node influence is fundamental for identifying key nodes in complex networks. Existing methods typically rely on generic indicators to rank node influence across diverse networks, thereby ignoring the individualized features of…
Complex networks have attracted increasing interest from various fields of science. It has been demonstrated that each complex network model presents specific topological structures which characterize its connectivity and dynamics. Complex…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
Network complexity has been studied for over half a century and has found a wide range of applications. Many methods have been developed to characterize and estimate the complexity of networks. However, there has been little research with…
We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for…
Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency…
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…
By studying varies dynamical processes, including coupled maps, cellular automata and coupled differential equations, on five different kinds of known networks, we found a positive relation between signal correlation and node's degree. Thus…
We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is…
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. The dynamics of the neurons is described by a set of stochastic differential equations in discrete time. The neurons interact…