Advances in Complex Systems

We propose that genetic encoding of self-assembling components greatly enhances the evolution of complex systems and provides an efficient platform for inductive generalization, i.e. the inductive derivation of a solution to a problem with a potentially infinite number of instances from a limited set of test examples. We exemplify this in simulations by evolving scalable circuitry for several problems. One of them, digital multiplication, has been intensively studied in recent years, where hitherto the evolutionary design of only specific small multipliers was achieved. The fact that this and other problems can be solved in full generality employing self-assembly sheds light on the evolutionary role of self-assembly in biology and is of relevance for the design of complex systems in nano- and bionanotechnology.

A discrete nonlinear model is studied and sufficient conditions which guarantee the permanence of the model are obtained. Assuming that the coefficients in the model are periodic, the existence of periodic solutions are obtained. Sufficient conditions are obtained to ensure the global stability of the positive periodic solution by constructing a suitable Lyapunov function.

Non-autonomous single-species growth chemostat models with general response functions are considered. In the models, the dilution rate and removal rate are allowed to be different from each other. A series of new criteria on the boundedness, permanence, persistence, average persistence and extinction of the population is established. In particular, when models degenerate into the almost periodic case, the equivalences of the permanence, persistence and average persistence of species are obtained. These results improve and extend some well-known corresponding results obtained in Refs. 1, 14 and 17.

We introduce an agent-based, evolutionary model of decisions inspired by the increasing return theory. Agents have to choose between options taking into account their own preferences and externalities from their neighbors. The aim is to analyze the distribution of decisions in a square lattice domain and its dependence on the initial conditions. Numerical results show that an undesirable option may be adopted by the majority and may lock in markets by means of clever or lucky movements done at the beginning.

This paper is devoted to the investigation of the oscillation of a class of second-order nonlinear impulsive delay difference equations. Some interesting results are obtained, and some examples which illustrate that impulsive perturbations play a very important role in giving rise to oscillations of equations are also included.

The purpose of the present study is to investigate the existence of deterministic chaos in the time series of occurrence or non-occurrence of severe thunderstorms of the pre-monsoon season over the Northeastern part of India. Results from the current study reveal the existence of chaos in the relevant time series. The corresponding predictabilities are also computed quantitatively. The study recommends that the formulation of numerical weather prediction models for forecasting the occurrence of this high frequency meso-scale convective system must take into account the intrinsic chaos.

We establish a discrete time non-autonomous two-species mutualistic system with delays by considering the influence of many generations on the density of species population. With the help of the method of coincidence degree and some techniques, an easily verifiable sufficient condition is derived for the existence of at least one positive periodic solution of the above system. Biological interpretations of the main result are also given.

This study aims to develop a realistic mathematical model of fabric. In contrast to other studies on fabric modeling as a deformable surface, the model described in this article takes into account the geometry of the object. Moreover, it integrates the nonlinear phenomena of the dynamic behavior of material. As input parameters, the weaving data that define the 3D structure of the object and the mechanical properties of the yarn that express its dynamics are used. Thus, the fabric model is composed of a geometrical model of fabric (structure) on which a model of yarn (material characterization) is added. This hypothesis may be reasonable since a fabric shows the result of a three-dimensional assembly of yarns judiciously disposed. Since these yarns interact dynamically: the main difficulty consists of defining the yarn model. In our case, it is composed of various nonlinear functions representing the dynamic behavior of yarn. In order to characterize the flexibility of material, the weight, the elasticity and any other mechanical characteristics defining the relation between the strain and the stretching out of the shape should be taken into account. Firstly, several works dealing with realistic mathematical models of fabric are described. A taxonomic classification is achieved in order to position our study (in comparison to the scientific community). Secondly, the model of the fabric is described. A geometrical model of the object is presented. It allows one to dimension the object in a 3D space and then to position it at its initial state. Subsequently, a nodal model of yarns is described, step by step, in order to demonstrate the separability of the various dynamic behaviors. These nodal links make it simple to integrate the proposed model in the global geometrical model. Thus, the methods of numerical resolution used to simulate the complete model of the fabric are exposed. One method is selected and used in order to improve the performances of the fabric simulator and to obtain better stability. Several simulations illustrate the quality of the results obtained.

Western harmony is comprised of sequences of chords, which obey grammatical rules. It is of interest to develop a compact representation of the harmonic movement of chord sequences. Here, we apply an approach from analysis of complex networks, known as "network motifs" to define repeating dynamical patterns in musical harmony. We describe each piece as a graph, where the nodes are chords and the directed edges connect chords which occur consecutively in the piece. We detect several patterns, each of which is a walk on this graph, which recur in diverse musical pieces from the Baroque to modern-day popular music. These patterns include cycles of three or four nodes, with up to two mutual edges (edges that point in both directions). Cliques and patterns with more than two mutual edges are rare. Some of these universal patterns of harmony are well known and correspond to basic principles of music theory such as hierarchy and directionality. This approach can be extended to search for recurring patterns in other musical components and to study other dynamical systems that can be represented as walks on graphs.

Iterated function system (IFS) models have been explored to represent discrete sequences where the attractor of an IFS is self-affine either in R² or R³ (R is the set of real numbers). In this paper, the self-affine IFS model is extended from R³ to Rⁿ (n is an integer and greater than 3), which is called the multi-dimensional self-affine fractal interpolation model. This new model is presented by introducing the defined parameter "mapping partial derivative." A constrained inverse algorithm is given for the identification of the model parameters. The values of new model depend continuously on all of the variables. That is, the function is determined by the coefficients of the possibly multi-dimensional affine maps. So the new model is presented as much more general and significant.

We have analyzed the relations between the mutational pressure, recombination and selection pressure in the bit-string model with sexual reproduction. For specific sets of these parameters, we have found three phase transitions with one phase where populations can survive. In this phase, recombination enhances the survival probability. Even if recombination is associated, to some extent, with additional mutations it could be advantageous to reproduction, indicating that the frequencies of recombinations and recombination-associated mutations can self-organize in Nature. Partitioning the diploid genome into pairs of chromosomes independently assorted during gamete production enables recombinations between groups of genes without the risk of mutations and is also advantageous for the strategy of sexual reproduction.