We study two dynamical properties of linear D-dimensional cellular automata over Zm namely, denseness of periodic points and topological mixing. For what concerns denseness of periodic points, we complete the work initiated in (Theoret. Comput. Sci. 174 (1997) 157, Theoret. Comput. Sci. 233 (1–2) (2000) 147, 14th Annual Symp. on Theoretical Aspects of Computer Science (STACS ’97), LNCS n. 1200,...

This paper studies mutually coupled integrateand-fire type chaotic oscillators. The coupling is realized by impulsive switchings and the system exhibits various synchronous and asynchronous phenomena. We give a basic classification of the chaos synchronization phenomena and their breakdown patterns. The stability of the synchronous states can be confirmed using the piecewise exact solutions, an...

We consider the 3-body problem in relativistic lineal [i.e., (1+1)-dimensional] gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly bound orbits of higher frequency compared to their nonrelativistic counterparts, as energy increases we find in the equal-mass case no evidence for either global chaos or a breakd...

We study the onset of eigenstate thermalization in the two-dimensional transverse field Ising model (2D-TFIM) in the square lattice. We consider two nonequivalent Hamiltonians: the ferromagnetic 2D-TFIM and the antiferromagnetic 2D-TFIM in the presence of a uniform longitudinal field. We use full exact diagonalization to examine the behavior of quantum chaos indicators and of the diagonal matri...

It is of vital importance to exactly estimate the unknown parameters of chaotic systems in chaos control and synchronization. In this paper, we present a method for estimating one-dimensional discrete chaotic system based on mean value method MVM . It is proposed by exploiting the ergodic and synchronization features of chaos. It can effectively estimate the parameter value, and it is more exac...

We discuss the problem of static chaos in spin glasses. In the case of magnetic eld perturbations, we propose a scaling theory for the spin-glass phase. Using the meaneld approach we argue that some pure states are suppressed by the magnetic eld and their free energy cost is determined by the nite-temperature xed point exponents. In this framework, numerical results suggest that meaneld chaos e...

In this paper, the method to control chaos by using phase space compression is applied to economic systems. Because of economic significance of state variable in economic dynamical systems, the values of state variables are positive due to capacity constraints and financial constraints, we can control chaos by adding upper bound or lower bound to state variables in economic dynamical systems, w...

Liu [Liu Rui, Coexistence of multifarious exact nonlinear wave solutions for generalized b-equation, Inter. J. Bifurcation and Chaos, 20, pp. 3193-3208, 2010] investigated the coexistence of multifarious exact traveling wave solutions of the generalized b-equation, and also presented three conjectures and two questions. In this note, by using the method of complete discrimination system for pol...

Emergent behaviors of collective intelligence systems, exemplified by swarm model, have attracted broad interests in recent years. However, current research mostly stops at observational interpretations and qualitative descriptions of emergent phenomena, and is essentially short of quantitative analysis and evaluation. In this paper, we conduct a quantitative study on the emergence of swarm mod...