Complex reactive dynamics on low-dimensional lattices is studied using mean-field models and Monte Carlo simulations. A lattice-compatible reactive scheme that gives rise to limit cycle behavior is constructed, involving a quadrimolecular reaction step and bimolecular adsorption and desorption steps. The resulting lattice limit cycle model is dissipative and, in the mean-field limit, exhibits sustained oscillations of the species concentrations for a wide range of parameter values. Lattice Monte Carlo simulations of the lattice limit cycle model show locally the emergence of sustained oscillations of the species concentrations. Random fluctuations of the concentrations, clustering between homologous species, and competition between the various clusters/species cause the in-phase oscillations of neighboring sites. Distant regions oscillate out of phase and spatial correlations decay exponentially with the distance. The amplitude and period of the local oscillations depend on the system parameters.

Using the example of two coupled logistic maps, we investigate the effect of nonidentical subsystems on the bifurcations of saddle periodic orbits embedded in a symmetric chaotic attractor. These bifurcations determine the process of loss of chaos synchronization. We show that if bifurcations conditioned by the symmetry of the system take part in the synchronization loss process, nonidentity changes the bifurcation scenario of the transition to a nonsynchronous regime. In this case, for example, the transition to the bubbling behavior is determined not by bifurcation of an orbit embedded in the chaotic attractor but by the smooth shift of it and the saddle-repeller bifurcation of the birth of new orbits in the vicinity of the quasisymmetric region.

In the work we investigate the bifurcational mechanism of the loss of stability of the synchronous chaotic regime in coupled identical systems. We show that loss of synchronization is a result of the sequence of soft bifurcations of saddle periodic orbits which induce the bubbling and riddling transitions in the system. A bifurcation of a saddle periodic orbit embedded in the chaotic attractor determines the bubbling transition. The phenomenon of riddled basins occurs through a bifurcation of a periodic orbit located outside the symmetric subspace.[S0031-9007 (97)03692-2] PACS numbers: 05.45. + bInteractive chaotic systems are known to demonstrate the chaotic synchronization phenomenon [1][2][3][4][5][6][7]. In the case of identical systems a synchronous regime corresponds to a chaotic attractor that locates in the symmetric subspace x 1 x 2 of the whole phase space of the system. When the system exits from the synchronization region, the chaotic attractor loses its stability in the normal to the subspace direction according to the determined scenario [8][9][10][11]. In this case bubbling and riddling transitions can be observed as intermediate stages. After bubbling transition the intermittent transient process can take place in the system. There are orbits repelled from the chaotic attractor and returned to the vicinity of the symmetric subspace. In this situation the noise of small intensity induces the so-called bubbling attractor [8]. After riddling transition in the basin of the symmetric chaotic attractor (including small neighborhood of an attractor) there appears a set of "holes" which belongs to the basin of other attractor [12 -14].These phenomena take place in different systems and are intensively investigated for the last time [8][9][10][11][12][13][14][15][16][17][18][19].The loss of stability of the chaotic state in the normal direction is immediately connected with bifurcations of saddle periodic orbits embedded in the symmetric chaotic attractor. For instance, in the work [17] it was demonstrated that riddling transition in a symmetric system appears as a result of saddle-repeller subcritical bifurcation (the eigenvalue 11) of the saddle fixed point embedded in the chaotic attractor.In this work we investigate the mechanism of the stability loss of the chaotic in-phase regime in the coupled logistic maps. We demonstrate that the loss of synchronization is a result of a sequence of soft bifurcations of the certain family of saddle periodic orbits. These bifurcations induce bubbling and riddling transitions in the system. A bifurcation of a saddle periodic orbit embedded in the chaotic attractor determines the bubbling transition. The phenomenon of riddled basins occurs through a bifurcation of a periodic orbit located outside the symmetric subspace.

No abstract