International Journal of Modern Physics C

Recurrence Plot (RP) and Recurrence Quantification Analysis (RQA) are signal numerical analysis methodologies able to work with nonlinear dynamical systems and nonstationarity. Moreover, they well evidence changes in the states of a dynamical system. We recall their features and give practical recipes. It is shown that RP and RQA detect the critical regime in financial indices (in analogy with phase transition) before a bubble bursts, whence allowing to estimate the bubble initial time. The analysis is made on DAX and NASDAQ daily closing price between January 1998 and November 2003. DAX is studied in order to set-up overall considerations, and as a support for deducing technical rules. The NASDAQ bubble initial time has been estimated to be on 19 October 1999.

The Heider balance (HB) is investigated in a fully connected graph of N nodes. The links are described by a real symmetric array r (i, j), i, j =1, …, N. In a social group, nodes represent group members and links represent relations between them, positive (friendly) or negative (hostile). At the balanced state, r (i, j) r (j, k) r (k, i) > 0 for all the triads (i, j, k). As follows from the structure theorem of Cartwright and Harary, at this state the group is divided into two subgroups, with friendly internal relations and hostile relations between the subgroups. Here the system dynamics is proposed to be determined by a set of differential equations, . The form of equations guarantees that once HB is reached, it persists. Also, for N =3 the dynamics reproduces properly the tendency of the system to the balanced state. The equations are solved numerically. Initially, r (i, j) are random numbers distributed around zero with a symmetric uniform distribution of unit width. Calculations up to N =500 show that HB is always reached. Time τ(N) to get the balanced state varies with the system size N as N^-1/2. The spectrum of relations, initially narrow, gets very wide near HB. This means that the relations are strongly polarized. In our calculations, the relations are limited to a given range around zero. With this limitation, our results can be helpful in an interpretation of some statistical data.

In this paper, we applied the Sato–Crutchfield equation to population genetics. We studied it analytically and numerically. It is applied to some cases in population of one locus with two alleles. It is found that Sato–Crutchfield equation does not affect the stability of the evolutionary equations but the reinforcement of the choice of heterozygote state.

We present the results of extensive numerical integration in (1 +1) dimensions of a set of continuum equations which was recently proposed for describing the growth of thin composite solid films composed of two types of particles. In this model, the Kardar–Parisi–Zhang (KPZ) equation, which describes the growth of the films, is coupled to the time-dependent Ginzburg–Landau (TDGL) equation for the order parameter. We study the effect of the model's parameters on the universality of the scaling exponents that characterize the power-law behavior of the various properties of interest, and the transitions in the films' morphology that result from varying the parameters. We find that the scaling properties of the model are nonuniversal. Phase diagrams that identify the various scaling regimes, as well as the morphological transitions, are obtained. Thus, neither the dynamics of the domains' growth is governed by the TDGL equation, nor is the scaling of the films' surface structure described by the KPZ equation.

Time evolutions of the circular cellular automata (CCA) are studied. The pattern seems to reach a dynamic balance state after several iterations in a fixed space. The time variations of population of each quadrant obey the famous logistic equation. It is found that although the initial patterns are very sensitive to the location of the first ring and the growth sequence, the dynamic patterns are independent of them. We propose that the CCA model may be used to simulate the evolution of biology.

In this article, we propose a high order method for solving steady and unsteady two-dimensional laminar boundary-layer equations. This method is convergent of sixth-order of accuracy. It is shown that this method is unconditionally stable. The unsteady separated stagnation point flow, the Falkner–Skan equation and Blasius equation are considered as special cases of these equations. Numerical experiments are given to illustrate our method and its convergence.

Similar to biological evolution and speciation, we define a language through a string of 8 or 16 bits. The parent gives its language to its children, apart from a random mutation from zero to one or from one to zero; initially all bits are zero. The Verhulst deaths are taken as proportional to the total number of people, while in addition languages spoken by many people are preferred over small languages. For a fixed population size, a sharp phase transition is observed: For low mutation rates, one language contains nearly all people; for high mutation rates, no language dominates and the size distribution of languages is roughly log-normal as for present human languages. A simple scaling law is valid.

The purpose of this paper is to investigate the length scale effects of small protein folding by lattice modeling. Heat capacity is computed to analyze folding transition temperature of the model proteins of different lengths. The results show that there is an evident phase transition when the lengths of the model proteins are similar to those of foldons. Furthermore, it is found that the folding transition temperature is proportional to the sequence length.

A cellular automata model is developed aiming to study the epidemic on a lattice of two dimensions. The characteristics of individual including reproduction, death by inherited diseases and age are studied in the Penna model. The spreading of epidemic and the reproduction of individual are considered as cellular automata. We shall mainly discuss the influence on the number of epidemical patients by infection rate and death rate. The results show that the existence of epidemic mainly depends on the infection rate and the death rate but not the initial ratio of patients. There are two reasons for nonexistent epidemic. As long as the infection rate is less than 0.3, the epidemic cannot spread. On the other hand, if the infection rate and the death rate are both high, the individuals with epidemic die out and the epidemic cannot spread, either. The epidemic can exist all along when the combination of infection rate and death rate are in the mid area.

We present a simulation model based on the Penna model to study the population evolution. The wealth of the individual is considered in the model. We define increasing ratio α and decreasing ratio β of the wealth presenting the individual wealth variation, also define minimum wealth PROMO which works when one reproduces. We study the influence of α and β on a species' survival or downfall, and the influence of PROMO on the age distribution of a species. According to the different values of α and β, we find diverse regimes where a species will survive or die out, and even the regime where species' survival or downfall are very sensitive. We study the relation between life expectancy and the wealth of the individual, finding that life expectancy doesn't increase but decrease a little when the wealth of the individual increases.

Recently, a new hyperchaos generator, obtained by controlling a three-dimensional autonomous chaotic system — Chen's system — with a periodic driving signal, has been found. In this letter, we formulate and study the hyperchaotic behaviors in the corresponding fractional-order hyperchaotic Chen's system. Through numerical simulations, we found that hyperchaos exists in the fractional-order hyperchaotic Chen's system with order less than 4. The lowest order we found to have hyperchaos in this system is 3.4. Finally, we study the synchronization problem of two fractional-order hyperchaotic Chen's systems.

A set of Benzorod arrays on a graphene substrate has been investigated by performing classical molecular-dynamics simulations. Benzorod is composed of aligned and dehydrogenated benzene rings that are stacked to form a rod-like structure. It has been found that the arrays considered are thermally stable up to elevated temperatures, with a dependence on length.