细胞神经网络的指数稳定性

该文研究了具有可变时滞的随机细胞神经网络的指数 稳定性,应用Razumikhin定理与Lyapunov函数,建立了这种细胞神经网络均方指数稳定与几乎必然指数稳定的两类判据,一类是时滞无关而另一类是时滞相关.     

Lattice games without rational strategies

We show that the lattice games of Guo and Miller support universal computation, disproving their conjecture that all lattice games have rational strategies. We also state an explicit counterexample to that conjecture: a three dimensional lattice game whose set of winning positions does not have a rational generating function.     

Evolution of groups with a hierarchical structure

The universal occurrence of a hierarchical structure and its dynamic behavior in various types of group, living or abstract, are discussed. Here the word “group” refers not only to tangible aggregation but also to invisible aggregation of social psychological and of geopolitical meaning. The evolution of these groups is simulated using a model of agents distributed on the lattices of cellular grids. It is assumed that agents, fearing isolation, interact asymmetrically with each other with regard to exchange of “power”. As an indicator of hierarchy, the Gini coefficient is introduced. Example calculations are made for the aggregation, fusion and fission of animal groups, and for the appearance of a powerful empire and the rise and fall of supremacy. It is shown that such abstract objects evolve with time in accordance with the universal rules of groups common to birds and fish.     

The unstable behavior of cellular premixed flames induced by intrinsic instability

The unstable behavior of cellular premixed flames induced by intrinsic instability is studied by two-dimensional unsteady calculations of reactive flows. In the present numerical simulation, the compressible Navier–Stokes equation including a one-step irreversible chemical reaction is employed. We consider two basic types of phenomena to account for the intrinsic instability of premixed flames, i.e., hydrodynamic and diffusive-thermal effects. The hydrodynamic effect is caused by the thermal expansion through the flame front; the diffusive-thermal effect is caused by the preferential diffusion of mass versus heat. A disturbance with several wavelength components is superimposed on a planar flame, and the formation of a cellular flame induced by hydrodynamic and diffusive-thermal effects is numerically simulated. After the cellular-flame formation, the combination and division of cells are observed. The behavior of cellular-flame fronts becomes more unstable when the Lewis number is lower than unity, since the diffusive-thermal effect has a great influence on the unstable behavior. The cell size changes with time, and its average is greater than the critical wavelength and becomes smaller by decreasing the Lewis number. The flame velocity of cellular flames depends strongly on the length of computational domain in the direction tangential to the flame front. As the length of computational domain increases, the flame velocity becomes larger. This is because the long-wavelength components of disturbances play an important role in the shape of cellular flames, i.e., in the flame-surface area.     

The finite-size scaling study of the specific heat and the Binder parameter for the six-dimensional Ising model

The six-dimensional Ising model with nearest-neighbor pair interactions is simulated on the Creutz cellular automaton by using the finite-size lattices with the linear dimensions L=4,6,8,10. The temperature variations and the finite-size scaling plots of the specific heat and Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature. The approximate values for the critical temperature of the infinite lattice T_C=10.838(1), T_C=10.836(20) and T_C=10.835(1) are obtained from the intersection points of specific heat curves, Binder parameter curves and the straight line fit of specific heat maxima, respectively. These results are in agreement with the more precise value of T_C=10.835(5). The value obtained for the critical exponent of the specific heat, i.e., =0.012(2) is also in agreement with =0 predicted by the theory.     

The dynamics of defect ensembles in one-dimensional cellular automata

We investigate the dynamics of ensembles of diffusive defects in one-dimensional deterministic cellular automata. The work builds on earlier results on individual random walks in cellular automata. Here we give a natural condition guaranteeing diffusive behavior also in the presence of other defects. Simple branching and birth mechanisms are introduced and prototype classes of cellular automata exhibiting weakly interacting walks capable of annihilation and coalescence are studied. Their equilibrium behavior is also characterized. The design principles of cellular automata with desired diffusive interaction properties become transparent from this analysis.     

Rotators,periodicity, and absence of diffusion in cyclic cellular automata

Cyclic cellular automata are two-dimensional cellular automata which generalize lattice versions of the Lorentz gas and certain biochemistry models of artificial life. We show that rotators and time reversibility play a special role in the creation of closed orbits in cyclic cellular automata. We also prove that almost every orbit is closed (periodic) and the absence of diffusion for the flipping rotator model (also known as the ant).     

Evolution by damage spreading in Kauffman model

In Kauffman's Boolean automata model on the square lattice, the Darwinian fitness of survival can be defined as the fraction of elements which do not change from one iteration to the next. Biological mutations are simulated by filpping one bit in the rule of one site. Selection of the fitter mutant then optimizes the whole lattice completely. This optimization is particularly effective near the critical point of the transition to chaos, but is in itself not a critical phenomenon. Also a two-dimensional spin glass can be optimized in this way.     

Self-averaging in complex brain neuron signals

Nonlinear statistical properties of Ventral Tegmental Area (VTA) of limbic brain are studied in vivo. VTA plays key role in generation of pleasure and in development of psychological drug addiction. It is shown that spiking time-series of the VTA dopaminergic neurons exhibit long-range correlations with self-averaging behavior. This specific VTA phenomenon has no relation to VTA rewarding function. Last result reveals complex role of VTA in limbic brain. Received 17 April 2002 / Received in final form 30 September 2002 Published online 31 December 2002     

Local structure theory: Calculation on hexagonal arrays,and interaction of rule and lattice

Local structure theory calculations⁷ are applied to the study of cellular automata on the two-dimensional hexagonal lattice. A particular hexagonal lattice rule denoted (3422) is considered in detail. This rule has many features in common with Conway'sLife. The local structure theory captures many of the statistical properties of this rule; this supports hypotheses raised by a study ofLife itself⁽⁶⁾. As inLife, the state of a cell under (3422) depends only on the state of the cell itself and the sum of states in its neighborhood at the previous time step. This property implies that evolution rules which operate in the same way can be studied on different lattices. The differences between the behavior of these rules on different lattices are dramatic. The mean field theory cannot reflect these differences. However, a generalization of the mean field theory, the local structure theory, does account for the rule-lattice interaction.