Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGeneral coevolution of topology and dynamics in networks
156
0
0.0
(
0
)
Added by
Jose Luis Herrera Diestra Mr.
Publication date
2011
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We present a general framework for the study of coevolution in dynamical systems. This phenomenon consists of the coexistence of two dynamical processes on networks of interacting elements: node state change and rewiring of links between nodes. The process of rewiring is described in terms of two basic actions: disconnection and reconnection between nodes, both based on a mechanism of comparison of their states. We assume that the process of rewiring and node state change occur with probabilities Pr and Pc respectively, independent of each other. The collective behavior of a coevolutionary system can be characterized on the space of parameters (Pr, Pc). As an application, for a voterlike node dynamics we find that reconnections between nodes with similar states lead to network fragmentation. The critical boundaries for the onset of fragmentation in networks with different properties are calculated on this space. We show that coevolution models correspond to curves on this space describing functional relations between Pr and Pc. The occurrence of a one-large-domain phase and a fragmented phase in the network is predicted for diverse models, and agreement is found with some earlier results. The collective behavior of system is also characterized on the space of parameters for the disconnection and reconnection actions. In a region of this space, we find a behavior where different node states can coexist for very long times on one large, connected network.
rate research
Read More
Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the complex set of coupling they exhibit, the latter being modeled by complex networks. The dynamical behavior of the system and the topology of the underlying network are strongly intertwined, raising the question of the optimal architecture that makes synchronization robust. The Master Stability Function (MSF) has been proposed and extensively studied as a generic framework to tackle synchronization problems. Using this method, it has been shown that for a class of models, synchronization in strongly directed networks is robust to external perturbations. In this paper, our approach is to transform the non-autonomous system of coupled oscillators into an autonomous one, showing that previous results are model-independent. Recent findings indicate that many real-world networks are strongly directed, being potential candidates for optimal synchronization. Inspired by the fact that highly directed networks are also strongly non-normal, in this work, we address the matter of non-normality by pointing out that standard techniques, such as the MSF, may fail in predicting the stability of synchronized behavior. These results lead to a trade-off between non-normality and directedness that should be properly considered when designing an optimal network, enhancing the robustness of synchronization.
In this work we present a general mechanism by which simple dynamics running on networks become self-organized critical for scale free topologies. We illustrate this mechanism with a simple arithmetic model of division between integers, the division model. This is the simplest self-organized critical model advanced so far, and in this sense it may help to elucidate the mechanism of self-organization to criticality. Its simplicity allows analytical tractability, characterizing several scaling relations. Furthermore, its mathematical nature brings about interesting connections between statistical physics and number theoretical concepts. We show how this model can be understood as a self-organized stochastic process embedded on a network, where the onset of criticality is induced by the topology.
We study the consequences of introducing individual nonconformity in social interactions, based on Axelrods model for the dissemination of culture. A constraint on the number of situations in which interaction may take place is introduced in order to lift the unavoidable ho mogeneity present in the final configurations arising in Axelrods related models. The inclusion of this constraint leads to the occurrence of complex patterns of intracultural diversity whose statistical properties and spatial distribution are characterized by means of the concepts of cultural affinity and cultural cli ne. It is found that the relevant quantity that determines the properties of intracultural diversity is given by the fraction of cultural features that characterizes the cultural nonconformity of individuals.
The features of animal population dynamics, for instance, flocking and migration, are often synchronized for survival under large-scale climate change or perceived threats. These coherent phenomena have been explained using synchronization models. However, such models do not take into account asynchronous and adaptive updating of an individuals status at each time. Here, we modify the Kuramoto model slightly by classifying oscillators as leaders or followers, according to their angular velocity at each time, where individuals interact asymmetrically according to their leader/follower status. As the angular velocities of the oscillators are updated, the leader and follower status may also be reassigned. Owing to this adaptive dynamics, oscillators may cooperate by taking turns acting as a leader or follower. This may result in intriguing patterns of synchronization transitions, including hybrid phase transitions, and produce the leader-follower switching pattern observed in bird migration patterns.
We use a stochastic Markovian dynamics approach to describe the spreading of vector-transmitted diseases, like dengue, and the threshold of the disease. The coexistence space is composed by two structures representing the human and mosquito populations. The human population follows a susceptible-infected-recovered (SIR) type dynamics and the mosquito population follows a susceptible-infected-susceptible (SIS) type dynamics. The human infection is caused by infected mosquitoes and vice-versa so that the SIS and SIR dynamics are interconnected. We develop a truncation scheme to solve the evolution equations from which we get the threshold of the disease and the reproductive ratio. The threshold of the disease is also obtained by performing numerical simulations. We found that for certain values of the infection rates the spreading of the disease is impossible whatever is the death rate of infected mosquito.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
