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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.

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Two resistively coupled Chua's circuits are studied in this paper. We consider the case when the two circuits are identical, and the case when there is a detuning between the basic frequencies of the two circuits. In the first case, the multistability (i.e. the coexistence of attractors) evolution scenario is studied. In the second case, we study the influence of detuning on the multistability, and on the mutual synchronization in the chaotic regimes. We present bifurcation diagrams of the main synchronization regions. We also compare the dynamics of coupled Chua's circuits with the dynamics of other coupled systems.

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