Related papers: Static Pairwise Annihilation in Complex Networks
This paper studies systems of particles following independent random walks and subject to annihilation, binary branching, coalescence, and deaths. In the case without annihilation, such systems have been studied in our 2005 paper…
We study the interplay between network topology and complex space-time patterns and introduce a concept to analytically predict complex patterns in networks of Stuart-Landau oscillators with linear symmetric and instantaneous coupling based…
The dynamical mechanisms that can stabilize the coexistence of species (or strategies) are of substantial interest for the maintenance of biodiversity and in sociobehavioural dynamics. We investigate the mean extinction time in the…
Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph…
The problem of reliability of a large distributed system is analyzed via a new mathematical model. A typical framework is a system where a set of files are duplicated on several data servers. When one of these servers breaks down, all…
We study the persistent recoverable prevalence and the extinction of computer viruses via e-mails on a growing scale-free network with new users, which structure is estimated form real data. The typical phenomenon is simulated in a…
An annealed version of the quenched mean-field model for epidemic spread is introduced and investigated analytically and assisted by numerical calculations. The interaction between individuals follows a prescription that is used to generate…
This paper continues our previous study on spreading processes in inhomogeneous populations consisting of susceptible and immune individuals [V. Blavatska, Yu. Holovatch, Physica A 573, 125980 (2021)]. A special role in such populations is…
After a failure or attack the structure of a complex network changes due to node removal. Here, we show that the degree distribution of the distorted network, under any node disturbances, can be easily computed through a simple formula.…
We study a population of $N$ particles, which evolve according to a diffusion process and interact through a dynamical network. In turn, the evolution of the network is coupled to the particles' positions. In contrast with the mean-field…
Annihilation processes, where the reacting particles are influenced by some external advective field, are one of the simplest examples of nonlinear statistical systems. This type of processes can be observed in miscellaneous chemical,…
We investigate mechanisms of the typically observed recoverable prevalence in epidemic spreading. Assuming the time-independent connectivity correlations, we analyze the dynamics of spreading on linearly growing scale-free (SF) networks,…
The spectrum of stable electrically and magnetically charged supersymmetric particles can change discontinuously due to the decay of these particles as the vacuum on the Coulomb branch is varied. We show that this decay process is well…
We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…
We investigate the kinetics of systems in which particles of one species undergo binary fragmentation and pair annihilation. In the latter, nonlinear process, fragments react at collision to produce an inert species, causing loss of mass.…
The pivotal quality of proximity graphs is connectivity, i.e. all nodes in the graph are connected to one another either directly or via intermediate nodes. These types of graphs are robust, i.e., they are able to function well even if they…
We discuss a reaction-diffusion model in one dimension subjected to an external driving force. Each lattice site may be occupied by at most one particle. The particles hop with asymmetric rates (the sum of which is one) to the right or left…
Discrete- and continuous-time approaches are frequently used to model the role of heterogeneity on dynamical interacting agents on the top of complex networks. While, on the one hand, one does not expect drastic differences between these…
While renormalization groups are fundamental in physics, renormalization of complex networks remains vague in its conceptual definition and methodology. Here, we propose a novel strategy to renormalize complex networks. Rather than…
Empirical estimation of critical points at which complex systems abruptly flip from one state to another is among the remaining challenges in network science. However, due to the stochastic nature of critical transitions it is widely…