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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.…
Competition and collaboration are at the heart of multi-agent probabilistic spreading processes. The battle on public opinion and competitive marketing campaigns are typical examples of the former, while the joint spread of multiple…
This article reviews and evaluates models of network evolution based on the notion of structural diversity. We show that diversity is an underlying theme of three principles of network evolution: the preferential attachment model,…
We consider the dynamics of a virus spreading through a population that produces a mutant strain with the ability to infect individuals that were infected with the established strain. Temporary cross-immunity is included using a time delay,…
As two main focuses of the study of complex networks, the community structure and the dynamics on networks have both attracted much attention in various scientific fields. However, it is still an open question how the community structure is…
The deep neural network has attained significant efficiency in image recognition. However, it has vulnerable recognition robustness under extensive data uncertainty in practical applications. The uncertainty is attributed to the inevitable…
We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection of appropriate active controls. While boundary controls alone prove inadequate for…
Reaction-diffusion systems may lead to the formation of steady state heterogeneous spatial patterns, known as Turing patterns. Their mathematical formulation is important for the study of pattern formation in general and play central roles…
The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability…
The microscopic and macroscopic dynamics of random networks is investigated in the strong-dilution limit (i.e. for sparse networks). By simulating chaotic maps, Stuart-Landau oscillators, and leaky integrate-and-fire neurons, we show that a…
We study the dynamical properties of a finite dynamical network composed of two interacting populations, namely; extrovert ($a$) and introvert ($b$). In our model, each group is characterized by its size ($N_a$ and $N_b$) and preferred…
We revisit two evolutionary game theory models, namely the Prisoner and the Snowdrift dilemmas, on top of small-world networks. These dynamics on networked populations (individuals occupying nodes of a graph) are mainly concerning on the…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
The Internet is a man-made complex system under constant attacks (e.g., Advanced Persistent Threats and malwares). It is therefore important to understand the phenomena that can be induced by the interaction between cyber attacks and cyber…
Network science has evolved into an indispensable platform for studying complex systems. But recent research has identified limits of classical networks, where links connect pairs of nodes, to comprehensively describe group interactions.…
In this work we study the behavior of classical two-person, two-strategies evolutionary games on a class of weighted networks derived from Barab\'asi-Albert and random scale-free unweighted graphs. Using customary imitative dynamics, our…
Network science investigates the architecture of complex systems to understand their functional and dynamical properties. Structural patterns such as communities shape diffusive processes on networks. However, these results hold under the…
We introduce and analyze a within-host dynamical model of the coevolution between rapidly mutating pathogens and the adaptive immune response. Pathogen mutation and a homeostatic constraint on lymphocytes both play a role in allowing the…
The networks of predator-prey interactions in ecological systems are remarkably complex, but nevertheless surprisingly stable in terms of long term persistence of the system as a whole. In order to understand the mechanism driving the…
Cascading failures and epidemic dynamics, as two successful application realms of network science, are usually investigated separately. How do they affect each other is still one open, interesting problem. In this letter, we couple both…