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Graphs are a highly expressive abstraction for modeling entities and their relations, such as molecular structures, social networks, and traffic networks. Deep Graph Networks (DGNs) have emerged as a family of deep learning models that can…
Theoretical modeling of computer virus/worm epidemic dynamics is an important problem that has attracted many studies. However, most existing models are adapted from biological epidemic ones. Although biological epidemic models can…
Nested structure, which is non-random, controls cooperation dynamics and biodiversity in plant-animal mutualistic networks. This structural pattern has been explained in a static (non-growth) network models. However, evolutionary processes…
The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations…
Understanding the pattern formation in communities has been at the center of attention in various fields. Here we introduce a novel model, called an "information-particle model," which is based on the reaction-diffusion model and the…
In many social complex systems, in which agents are linked by non-linear interactions, the history of events strongly influences the whole network dynamics. However, a class of "commonly accepted beliefs" seems rarely studied. In this…
The emergence of collective cooperation in competitive environments is a well-known phenomenon in biology, economics, and social systems. While most evolutionary game models focus on the evolution of strategies for a fixed game, how…
There are various examples of phenotypic plasticity in ecosystems that serve as the basis for a wide range of inducible defences against predation. These strategies include camouflage, burrowing, mimicry, evasive actions, and even…
Systems with simultaneous cooperation and competition among the elements are ubiquitous. In spite of their practical importance, knowledge on the evolution mechanism of this class of complex system is still very limit. In this work, by…
The dynamics of network formation are generally very complex, making the study of distributions over the space of networks often intractable. Under a condition called conservativeness, I show that the stationary distribution of a network…
This chapter introduces evolutionary antifragility as the time-scale interaction characteristics of a natural dynamic system. It describes the benefit derived from input distribution unevenness, based on the emergent system dynamics and its…
Biological networks have two modes. The first mode is static: a network is a passage on which something flows. The second mode is dynamic: a network is a pattern constructed by gluing functions of entities constituting the network. In this…
A common theme among the proposed models for network epidemics is the assumption that the propagating object, i.e., a virus or a piece of information, is transferred across the nodes without going through any modification or evolution.…
Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…
Epidemic processes are used commonly for modeling and analysis of biological networks, computer networks, and human contact networks. The idea of competing viruses has been explored recently, motivated by the spread of different ideas along…
We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great…
We study the dynamics of secondary infections on networks, in which only the individuals currently carrying a certain primary infection are susceptible to the secondary infection. In the limit of large sparse networks, the model is mapped…
Network structure plays a critical role in functionality and performance of network systems. This paper examines structural adaptivity of diffusively coupled, directed multi-agent networks that are subject to diffusion performance. Inspired…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by…