Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control

A new kind of generalized synchronization of two chaotic systems with uncertain parameters is proposed. Based on a pragmatical asymptotical stability theorem and an assumption of equal probability for ergodic initial conditions, an adaptive control law is derived so that it can be proved strictly that the common null solution of error dynamics and of parameter dynamics is actually asymptotically stable, i.e. these two identical systems are in generalized synchronization and the estimated parameters approach the uncertain values. It is called pragmatical generalized synchronization. Finally, two numerical examples are studied for two Quantum-CNN oscillator chaotic systems to show the effectiveness of the proposed generalized synchronization strategy with a double Duffing chaotic system as a goal system.     

Pattern memory analysis based on stability theory of cellular neural networks

In this paper, several sufficient conditions are obtained to guarantee that the n-dimensional cellular neural network can have even (?2ⁿ) memory patterns. In addition, the estimations of attractive domain of such stable memory patterns are obtained. These conditions, which can be directly derived from the parameters of the neural networks, are easily verified. A new design procedure for cellular neural networks is developed based on stability theory (rather than the well-known perceptron training algorithm), and the convergence in the new design procedure is guaranteed by the obtained local stability theorems. Finally, the validity and performance of the obtained results are illustrated by two examples.     

Genetic algorithms and cellular automata in aquifer management

A groundwater management problem is presented involving pumping cost minimization with both well discharges and well locations as decision variables. A grid of candidate well locations is set up and optimal arrangements of wells are sought within this discrete space. A genetic algorithm approach is presented with the following particular features: (a) A suitable scaling is applied to the objective function in order to alleviate its regionally flat behavior. (b) No penalty functions are involved in constraint handling. Instead, the feasible region is transformed into a rectangular domain. The transformation introduced is proved to be bijective. (c) A binary representation of well configurations is presented and compared to a combinatorial one. The binary representation necessitates the introduction of specially designed genetic operators. Besides purely genetic algorithms, the concept of cellular automaton is introduced as the basis of an alternative formulation of the optimization problem. The lattice of the cellular automaton provides the discrete set of candidate well positions. The well configuration is represented by a group of agents occupying an equal number of lattice sites. The agents change positions as dictated by the structure of the automaton and, also, by an associated genetic algorithm, which directs the evolution of the whole scheme toward an optimal configuration. An improved performance of this approach is noted and discussed in comparison to the purely genetic algorithm schemes of the present work. A simulated annealing approach is also applied to the same problem for comparison purposes. Finally, a new and more efficient hybrid annealing–genetic approach is introduced and discussed.     

LAND USE OPTIMIZATION USING SELF-ORGANIZING ALGORITHMS

ABSTRACT. In many spatial systems the interaction between various regions decreases dramatically with distance. This suggests that local trade-offs may be more important than global ones in land use planning and that a decentralized, parallel optimization of the individual regions may be an attractive supplement to more centralized optimization approaches. In this paper, we solve a forest planning problem using a series of decentralized approaches. The approaches can be characterized as self-organizing algorithms and are modeled in the framework of a cellular automaton. We compare our results with those obtained by more centralized approaches, viz. a large sample approach, simulated annealing, and a genetic algorithm. We find that the self-organizing algorithms generally converge much faster to solutions which are at least as good as those obtained by simulated annealing and the genetic algorithm.     

Deterministic one-dimensional cellular automata

A formal treatment of some of the properties of deterministic, rule 150, elementary one-dimensional cellular automata (CA) with null boundary conditions is presented. The general form of the characteristic polynomial of the CA global rule transition matrix is obtained. Mathematical relationships between the CA register lengths and the order of the corresponding group or semigroup structures are derived.     

On the decidability of the word problem for amalgamated free products of inverse semigroups

We study inverse semigroup amalgams [S ₁,S ₂;U], where S ₁ and S ₂ are finitely presented inverse semigroups with decidable word problem and U is an inverse semigroup with decidable membership problem in S ₁ and S ₂. We use a modified version of Bennett’s work on the structure of Schützenberger graphs of the ℛ-classes of S ₁* _U S ₂ to state sufficient conditions for the amalgamated free products S ₁* _U S ₂ having decidable word problem.     

Computer simulation of a cellular automata model for the immune response in a retrovirus system

Immune response in a retrovirus system is modeled by a network of three binary cell elements to take into account some of the main functional features of T4 cells, T8 cells, and viruses. Two different intercell interactions are introduced, one of which leads to three fixed points while the other yields bistable fixed points oscillating between a healthy state and a sick state in a mean field treatment. Evolution of these cells is studied for quenched and annealed random interactions on a simple cubic lattice with a nearest neighbor interaction using inhomogenous cellular automata. Populations of T4 cells and viral cells oscillate together with damping (with constant amplitude) for annealed (quenched) interaction on increasing the value of mixing probabilityB from zero to a characteristic valueB _ca (B _cq). For higherB, the average number of T4 cells increases while that of the viral infected cells decreases monotonically on increasingB, suggesting a phase transition atB _ca (B _cq).     

Porous product with reduced apparent density keeps good mechanical properties. Extruded composites of poly(vinyl chloride) blown under microwave irradiation

New foaming method, enhanced by microwave irradiation, was elaborated and applied to obtain porous poly(vinyl chloride) and its composites with fine cell structure. The so called “thermal runaway” effect was observed during the heating of poly(vinyl chloride) under microwave irradiation. The temperature of this effect decreases as a result of additives incorporation into polymer matrix. Microwave irradiation allowed effective heating of extruded poly(vinyl chloride) and its composites with carbon black (CB) filler, behind the extruder head and decomposing azodicarbonamide (ADC) to obtain porous products. The use of CB additive to poly(vinyl chloride) significantly increased its ability to be heated under microwave irradiation as well as improved the cell structure and decreased the apparent density of final products.Among additionally used fillers (1 wt%) the montmorillonite caused the apparent density decrease of foamed materials ca. 10%, however beneficially influenced on the quality of cells structure, giving the products with isotropic cells and the highest cell density as well as keeping the tensile strength on similar level as in the case of the materials with CB and ADC only.     

Simulation numérique des détonations à double structure cellulaireNumerical simulation of detonations with double cellular structure

We present the results of numerical two-dimensional simulations of detonation cellular structures under non-monotonous heat release provided by a chemical reaction comprising two successive exothermic steps. The influence of the rate of the second step of chemical reaction on the detonation cellular structure has been investigated. Our simulations are the first that reproduce a cellular structure composed of two clearly distinct sets of cells with different characteristic sizes where fine cells completely fill up larger ones, as has been observed experimentally. To cite this article: V. Guilly et al., C. R. Mecanique 334 (2006).