Phase Transition in Evolutionary Games

The evolution of cooperative behaviour is studied in the deterministic version of the Prisoners' Dilemma on a two-dimensional lattice. The payoff parameter is set at the critical region $1.8 < b < 2.0$ , where clusters of cooperators are formed in all spatial sizes. Using the factorial moments developed in particle and nuclear physics for the study of phase transition, the distribution of cooperators is studied as a function of the bin size covering varying numbers of lattice cells. From the scaling behaviour of the moments a scaling exponent is determined and is found to lie in the range where phase transitions are known to take place in physical systems. It is therefore inferred that when the payoff parameter is increased through the critical region the biological system of cooperators undergoes a phase transition to defectors. The universality of the critical behaviour is thus extended to include also this particular model of evolution dynamics.Comment: 12 pages + 3 figures, latex, submitted to Natur

Critical Behavior of Hadronic Fluctuations and the Effect of Final-State Randomization

The critical behaviors of quark-hadron phase transition are explored by use of the Ising model adapted for hadron production. Various measures involving the fluctuations of the produced hadrons in bins of various sizes are examined with the aim of quantifying the clustering properties that are universal features of all critical phenomena. Some of the measures involve wavelet analysis. Two of the measures are found to exhibit the canonical power-law behavior near the critical temperature. The effect of final-state randomization is studied by requiring the produced particles to take random walks in the transverse plane. It is demonstrated that for the measures considered the dependence on the randomization process is weak. Since temperature is not a directly measurable variable, the average hadronic density of a portion of each event is used as the control variable that is measurable. The event-to-event fluctuations are taken into account in the study of the dependence of the chosen measures on that control variable. Phenomenologically verifiable critical behaviors are found and are proposed for use as a signature of quark-hadron phase transition in relativistic heavy-ion collisions.Comment: 17 pages (Latex) + 24 figures (ps file), submitted to Phys. Rev.

Novel interface-selected waves and their influences on wave competitions

The topic of interface effects in wave propagation has attracted great attention due to their theoretical significance and practical importance. In this paper we study nonlinear oscillatory systems consisting of two media separated by an interface, and find a novel phenomenon: interface can select a type of waves (ISWs). Under certain well defined parameter condition, these waves propagate in two different media with same frequency and same wave number; the interface of two media is transparent to these waves. The frequency and wave number of these interface-selected waves (ISWs) are predicted explicitly. Varying parameters from this parameter set, the wave numbers of two domains become different, and the difference increases from zero continuously as the distance between the given parameters and this parameter set increases from zero. It is found that ISWs can play crucial roles in practical problems of wave competitions, e.g., ISWs can suppress spirals and antispirals

On delayed genetic regulatory networks with polytopic uncertainties: Robust stability analysis

Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we investigate the robust asymptotic stability problem of genetic regulatory networks with time-varying delays and polytopic parameter uncertainties. Both cases of differentiable and nondifferentiable time-delays are considered, and the convex polytopic description is utilized to characterize the genetic network model uncertainties. By using a Lyapunov functional approach and linear matrix inequality (LMI) techniques, the stability criteria for the uncertain delayed genetic networks are established in the form of LMIs, which can be readily verified by using standard numerical software. An important feature of the results reported here is that all the stability conditions are dependent on the upper and lower bounds of the delays, which is made possible by using up-to-date techniques for achieving delay dependence. Another feature of the results lies in that a novel Lyapunov functional dependent on the uncertain parameters is utilized, which renders the results to be potentially less conservative than those obtained via a fixed Lyapunov functional for the entire uncertainty domain. A genetic network example is employed to illustrate the applicability and usefulness of the developed theoretical results

The Relativistic Rotation

The classical rotation is not self-consistent in the framework of the special theory of relativity. the Relativistic rotation is obtained, which takes the relativistic effect into account. It is demonstrated that the angular frequency of classical rotation is only valid in local approximation. The properties of the relativistic rotation and the relativistic transverse Doppler shift are discussed in this work

Fluctuations of Spatial Patterns as a Measure of Classical Chaos

In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the logistic map and the Lorenz model) to check its effectiveness in characterizing the dynamical behaviors. It is found that the indices $\mu _q$ are as useful as the Lyapunov exponents in providing a quantitative measure of chaos.Comment: 10 pages + 7 figures (in ps file), LaTex, Submitted to Phys. Rev.