In this paper, we discuss distributive synchronization of complex networks in finite time, with a single nonlinear pinning controller. The results apply to heterogeneous dynamic networks, too. Different from many models, which assume the coupling matrix being symmetric (or the connecting graph is undirected), here, the coupling matrix is asymmetric (or the connecting graph is directed
The desynchronization problems in oscillatory networks is considered. A new desynchronization notion is introduced and desynchronization conditions are provided. The desynchronization notion is formulated in terms of Yakubovich oscillatority of the auxiliary synchronization error system. As an example, the network of diffusively coupled FitzHugh-Nagumo systems with undirected graph is considered. The simple inequality guaranteeing network desynchronization is derived. The simulation results confirm the validity of the obtained analytical results.
In this paper we investigate how so-called quorum-sensing networks can be de-synchronized. Such networks, which arise in many important application fields such as systems biology, are characterized by the fact that direct communication between network nodes is superimposed to communication with a shared, environmental, variable. In particular, we provide a new sufficient condition ensuring that the trajectories of these quorum-sensing networks diverge from their synchronous evolution. Then, we apply our result to study two applications.
We consider a continuous mathematical description of a population of ants and simulate numerically their foraging behavior using a system of partial differential equations of chemotaxis type. We show that this system accurately reproduces observed foraging behavior, especially spontaneous trail formation and efficient removal of food sources. We show through numerical experiments that trail formation is correlated with efficient food removal. Our results illustrate the emergence of trail formation from simple modeling principles.
Paul Anglin criticised our analysis of the neoclassical theory of the firm, but makes a number of incorrect assertions about our assumptions. We correct these misunderstandings, but acknowledge that one criticism he makes is correct. We correct this flaw with a new argument that supersedes the flawed strategic reaction argument we presented in our previous paper.
The aim of this short paper is to summarize my recent preprint (arXiv:1209.1112), in which I proposed a novel and probably controversial view about cognitive mapping; that is, the image of the city out of the underlying scaling of city artifacts or locations. The scaling refers to a recurring structure of far more small things than large ones. In this paper, I attempt to further clarify the central argument, and identify some possible areas of misunderstanding for readers.
A non stationary state in the one-dimensional infinite square well formed by a combination of the ground state and the first excited one is considered. The statistical complexity and the Fisher-Shannon entropy in position and momentum are calculated with time for this system. These measures are compared with the Heisenberg uncertainty relation, ΔxΔp. It is observed that the extreme values of ΔxΔp coincide in time with extreme values of the other two statistical magnitudes.
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
We make a short review about the synchronization in coupled phase oscillator models. Next, we study the common-noise-induced synchronization among active rotators. At an intermediate noise strength, the noise-induced synchronization takes place most effectively, which is analogous to the stochastic resonance. Finally, we study the synchronization of coupled phase oscillators with nonvariational interaction on scale-free networks. We find a sharp transition and a weak hysteresis in the nonvariational systems. The sharp transition is found also in the mean-field approximation.
The work presents two examples of simple mathematical formulas which are natural nonlinear modifications (one being a generalization) of Gielis' formula. These formulas involve a comparable number of parameters and provide non-Platonic representations of a vast diversity of natural shapes and patterns by incorporating diverse aspects of asymmetry and seeming disorder which are absent in the original Gielis' formula. It is also shown how diverse sequences resembling some natural-world pattern evolutions are also generated by such nonlinear formulas.
We study an evolutionary version of the Prisoner's Dilemma game, played by agents placed in a small-world network. Agents are able to change their strategy, imitating that of the most successful neighbor. We observe that different topologies, ranging from regular lattices to random graphs, produce a variety of emergent behaviors. This is a contribution towards the study of social phenomena and transitions governed by the topology of the community.
Statistical properties of the taxonomic classification of human languages are studied. It is shown that, at the highest levels of the taxonomic hierarchy, the frequency of taxon members as a function of the number of languages belonging to each member decays as a power law. This feature reveals that a self-similar structure underlies the taxonomy of languages, exactly as observed in the taxonomic classification of biological species. Such an analogy is a clue to the evolutionary foundation of language classification based on long-range comparison.
R. Castrejon Garcia, A. Sarmiento Galan, J. R. Castrejon Pita
et al.
We study the fractal dimension of the contour of the liquid-gas interface in a spray. Our images include both, the linking region and the break-up region and are obtained with a high-resolution shadowgraph technique; this means that the images can then be subject to an intensity filtering, equivalent to a threshold analysis, that enables the establishment of the fractal range.
This article gives a brief introduction to the mathematical modeling of large-scale biological evolution and extinction. We give three examples of simple models in this field: the coevolutionary avalanche model of Bak and Sneppen, the environmental stress model of Newman, and the increasing fitness model of Sibani, Schmidt, and Alstrom. We describe the features of real evolution which these models are intended to explain and compare the results of simulations against data drawn from the fossil record.
We introduce two three sided adaptative systems as toy models to mimic the exchange of commodities between buyers and sellers. These models are simple extensions of the minority game, exhibiting similar behaviour as well as some new features. The main difference between our two models is that in the first the three sides are equivalent while in the second, one choice appears as a compromise between the two other sides. Both models are investigated numerically and compared with the original minority game.
Clustering and correlation effects are frequently observed in chaotic systems in situations where, because of the positivity of the Lyapunov exponents, no dimension reduction is to be expected. In this paper, using a globally coupled network of Bernoulli units, one finds a general mechanism by which strong correlations and slow structures are obtained at the synchronization edge. A structure index is defined, which diverges at the transition points. Some conclusions are drawn concerning the construction of an ergodic theory of self-organization.
We present a theoretical as well as experimental investigation of a population of self-replicating segments of code subject to random mutation and survival of the fittest. Under the assumption that such a system constitutes a minimal system with characteristics of life, we obtain a number of statements on the evolution of complexity and the trade-off between entropy and information.
We investigate an simple evolutionary game of sequences and demonstrate on this example the structure of fitness landscapes in discrete problems. We show the smoothing action of the genotype-phenotype mapping which still makes it feasible for evolution to work. Further we propose the density of sequence states as a classifying measure of fitness landscapes.