Self-Organized Criticality Analysis of Earthquake Model Based on Heterogeneous Networks

The original Olami-Feder-Christensen (OFC) model, which displays a robust power-law behavior, is a quasistatic two-dimensional version of the Burridge--Knopoff spring-block model of earthquakes. In this paper, we introduce a modified OFC model based on heterogeneous network, improving the redistribution rule of the original model. It can be seen as a generalization of the original OFC model. We numerically investigate the influence of theparameters θ and β, which respectively control the intensity of the evolutivemechanism of the topological growth and the inner selection dynamicsin our networks, and find that there are two distinct phases in theparameter space (θ, β). Meanwhile, we study the influence of the control parameter a either. Increasing a, the earthquake behavior of the model transfers from local to global.     

Self-Organized Criticality in a Simple Neuron Model Based on Scale-Free Networks

A simple model for a set of interacting idealized neurons in scale-free networks is introduced. The basic elements of the model are endowed with the main features of a neuron function. We find that our model displays powerlaw behavior of avalanche sizes and generates long-range temporal correlation. More importantly, we find different dynamical behavior for nodes with different connectivity in the scale-free networks.     

Self-Organized Criticality in a Simple Neuron Model Based on Scale-Free Networks

A simple model for a set of interacting idealized neurons in scale-free networks is introduced. The basic elements of the model are endowed with the main features of a neuron function. We find that our model displays powerlaw behavior of avalanche sizes and generates long-range temporal correlation. More importantly, we find different dynamical behavior for nodes with different connectivity in the scale-free networks.     

Self-organized Criticality in an Integrate-and-Fire Neuron Model Based on Modified Aging Networks

Based on an integrate-and-fire mechanism, we investigate self-organized criticality of a simple neuron model on a modified BA scale-free network with aging nodes. In our model, we find that the distribution of avalanche size follows power-law behavior. The critical exponent τ depends on the aging exponent α. The structures of the network with aging of nodes change with an increase of α. The different topological structures lead to different behaviors in models of integrate-and-fire neurons.     

Effects of Aging and Self-organized Criticality in a Pulse-Coupled Integrate-and-Fire Neuron Model Based on Small World Networks

Effects of aging and self-organized criticality in a pulse-coupled integrate-and-fire neuron model based on small world networks have been studied. We give the degree distribution of aging network, average shortest path length, the diameter of our network, and the clustering coefficient, and find that our neuron model displays the power-law behavior, and with the number of added links increasing, the effects of aging become smaller and smaller. This shows that if the brain works at the self-organized criticality state, it can relieve some effects caused by aging.     

Self-organized Criticality in Hierarchical Brain Network

It is shown that the cortical brain network of the macaque displays a hierarchically clustered organization and the neuron network shows small-world properties. Now the two factors will be considered in our model and the dynamical behavior of the model will be studied. We study the characters of the model and find that the distribution of avalanche size of the model follows power-law behavior.     

A Modified Earthquake Model of Self-Organized Criticality on Small World Networks

A modified Olami-Feder-Christensen model of self-organized criticality on a square lattice with the properties of small world networks has been studied. We find that our model displays power-law behavior and the exponent τ of the model depends on φ, the density of long-range connections in our network.     

Self-organized Criticality in Hierarchical Brain Network

It is shown that the cortical brain network of the macaque displays a hierarchically clustered organization and the neuron network shows small-world properties. Now the two factors will be considered in our model and the dynamical behavior of the model will be studied. We study the characters of the model and find that the distribution of avalanche size of the model follows power-law behavior.     

Effects of Vertex Activity and Self-organized Criticality Behavior on a Weighted Evolving Network

Effects of vertex activity have been analyzed on a weighted evolving network. The network is characterized by the probability distribution of vertex strength, each edge weight and evolution of the strength of vertices with different vertex activities. The model exhibits self-organized criticality behavior. The probability distribution of avalanche size for different network sizes is also shown. In addition, there is a power law relation between the size and the duration of an avalanche and the average of avalanche size has been studied for different vertex activities.     

Self-organized Criticality in a Model Based on Neural Network

Based on the LISSOM neural network model, we introduce a model to investigate self-organized criticality in the activity of neural populations. The influence of connection (synapse) between neurons has been adequately considered in this model. It is found to exhibit self-organized criticality (SOC) behavior under appropriate conditions. We also find that the learning process has promotive influence on emergence of SOC behavior. In addition, we analyze the influence of various factors of the model on the SOC behavior, which is characterized by the power-law behavior of the avalanche size distribution.     

Effects of Vertex Activity and Self-organized Criticality Behavior on a Weighted Evolving Network

Effects of vertex activity have been analyzed on a weighted evolving network. The network is characterized by the probability distribution of vertex strength, each edge weight and evolution of the strength of vertices with different vertex activities. The model exhibits self-organized criticality behavior. The probability distribution of avalanche size for different network sizes is also shown. In addition, there is a power law relation between the size and the duration of an avalanche and the average of avalanche size has been studied for different vertex activities.     

Self-organized Criticality and Synchronization in a Pulse-coupled Integrate-and-Fire Neuron Model Based on Small World Networks

A lattice model for a set of pulse-coupled integrate-and-fire neurons with small world structure is introduced. We find that our model displays the power-law behavior accompanied with the large-scale synchronized activities among the units. And the different connectivity topologies lead to different behaviors in models of integrate-and-fire neurons.     

Robustness and Flexibility of Neural Function through Dynamical Criticality

In theoretical biology, robustness refers to the ability of a biological system to function properly even under perturbation of basic parameters (e.g., temperature or pH), which in mathematical models is reflected in not needing to fine-tune basic parameter constants; flexibility refers to the ability of a system to switch functions or behaviors easily and effortlessly. While there are extensive explorations of the concept of robustness and what it requires mathematically, understanding flexibility has proven more elusive, as well as also elucidating the apparent opposition between what is required mathematically for models to implement either. In this paper we address a number of arguments in theoretical neuroscience showing that both robustness and flexibility can be attained by systems that poise themselves at the onset of a large number of dynamical bifurcations, or dynamical criticality, and how such poising can have a profound influence on integration of information processing and function. Finally, we examine critical map lattices, which are coupled map lattices where the coupling is dynamically critical in the sense of having purely imaginary eigenvalues. We show that these map lattices provide an explicit connection between dynamical criticality in the sense we have used and “edge of chaos” criticality.     

Self-organized Criticality in an Earthquake Model on Random Network

A simplified Olami-Feder-Christensen model on a random network has been studied. We propose a new toppling rule — when there is an unstable site toppling, the energy of the site is redistributed to its nearest neighbors randomly not averagely. The simulation results indicate that the model displays self-organized criticality when the system is conservative, and the avalanche size probability distribution of the system obeys finite size scaling. When the system is nonconservative, the model does not display scaling behavior. Simulation results of our model with different nearest neighbors q is also compared, which indicates that the spatial topology does not alter the critical behavior of the system.     

Effects of Some Neurobiological Factors in a Self-organized Critical Model Based on Neural Networks

Based on an integrate-and-fire mechanism, we investigate the effect of changing the efficacy of the synapse,the transmitting time-delayed, and the relative refractoryperiod on the self-organized criticality in our neural network model.     

Effects of Some Neurobiological Factors in a Self-organized Critical Model Based on Neural Networks

Based on an integrate-and-fire mechanism, we investigate the effect of changing the efficacy of the synapse,the transmitting time-delayed, and the relative refractoryperiod on the self-organized criticality in our neural network model.     

Self-Organized Criticality in an Anisotropic Earthquake Model

We have made an extensive numerical study of a modified model proposed by Olami,Feder,and Christensen to describe earthquake behavior.Two situations were considered in this paper.One situation is that the energy of the unstable site is redistributed to its nearest neighbors randomly not averagely and keeps itself to zero.The other situation is that the energy of the unstable site is redistributed to its nearest neighbors randomly and keeps some energy for itself instead of reset to zero.Different boundary conditions were considered as well.By analyzing the distribution of earthquake sizes,we found that self-organized criticality can be excited only in the conservative case or the approximate conservative case in the above situations.Some evidence indicated that the critical exponent of both above situations and the original OFC model tend to the same result in the conservative case.The only difference is that the avalanche size in the original model is bigger.This result may be closer to the real world,after all,every crust plate size is different.     

Entropy,Economics, and Criticality

Information theory is a well-established method for the study of many phenomena and more than 70 years after Claude Shannon first described it in A Mathematical Theory of Communication it has been extended well beyond Shannon’s initial vision. It is now an interdisciplinary tool that is used from ‘causal’ information flow to inferring complex computational processes and it is common to see it play an important role in fields as diverse as neuroscience, artificial intelligence, quantum mechanics, and astrophysics. In this article, I provide a selective review of a specific aspect of information theory that has received less attention than many of the others: as a tool for understanding, modelling, and detecting non-linear phenomena in finance and economics. Although some progress has been made in this area, it is still an under-developed area that I argue has considerable scope for further development.     

Quantum Temporal Steering in a Dephasing Channel With Quantum Criticality

We investigate the quantum temporal steering (TS), i.e., a temporal analogue of Einstein‐Podolsky‐Rosen steering, in a dephasing channel which is modeled by a central spin half surrounded by a spin‐1/2 XY chain where quantum phase transition happens. The TS parameter and the TS weight are employed to characterize the TS dynamics. We analytically obtain the dependence of on the decoherence factor. The numerical results show an obvious suppression of and when the XY chain approaches to the critical point. In view of the significance of quantum channel, we develop a new concept, TS weight power, in order to quantify the capacity of the quantum channel in dominating TS behavior. This new quantity enables us to indicate the quantum criticality of the environment by the quantum correlation of TS in the coupled system.