The delay logistic map with two types of q-deformations: Tsallis and Quantum-group type are studied. The stability of the map and its bifurcation scheme is analyzed as a function of the deformation and delay feedback parameters. Chaos is suppressed i
n a certain region of deformation and feedback parameter space. The steady state obtained by delay feedback is maintained in one type of deformation while chaotic behavior is recovered in another type with increasing delay.
Recently, a novel mixed-synchronization phenomenon is observed in counter-rotating nonlinear coupled oscillators. In mixed-synchronization state: some variables are synchronized in-phase, while others are out-of-phase. We have experimentally verified
the occurrence of mixed-synchronization states in coupled counter-rotating chaotic piecewise Rossler oscillator. Analytical discussion on approximate stability analysis and numerical confirmation on the experimentally observed behavior is also given.
It was observed that the spatiotemporal chaos in lattices of coupled chaotic maps was suppressed to a spatiotemporal fixed point when some fraction of the regular coupling connections were replaced by random links. Here we investigate the effects of
different kinds of parametric fluctuations on the robustness of this spatiotemporal fixed point regime. In particular we study the spatiotemporal dynamics of the network with noisy interaction parameters, namely fluctuating fraction of random links and fluctuating coupling strengths. We consider three types of fluctuations: (i) noisy in time, but homogeneous in space; (ii) noisy in space, but fixed in time; (iii) noisy in both space and time. We find that the effect of different kinds of parameteric noise on the dy- namics is quite distinct: quenched spatial fluctuations are the most detrimental to spatiotemporal regularity; spatiotemporal fluctuations yield phenomena similar to that observed when parameters are held constant at the mean-value; and interestingly, spatiotemporal regularity is most robust under spatially uniform temporal fluctuations, which in fact yields a larger fixed point range than that obtained under constant mean-value parameters.
We investigate the spatiotemporal dynamics of a lattice of coupled chaotic maps whose coupling connections are dynamically rewired to random sites with probability p, namely at any instance of time, with probability p a regular link is switched to a
random one. In a range of weak coupling, where spatiotemporal chaos exists for regular lattices (i.e. for p = 0), we find that p > 0 yields synchronized periodic orbits. Further we observe that this regularity occurs over a window of p values, beyond which the basin of attraction of the synchronized cycle shrinks to zero. Thus we have evidence of an optimal range of randomness in coupling connections, where spatiotemporal regularity is efficiently obtained. This is in contrast to the commonly observed monotonic increase of synchronization with increasing p, as seen for instance, in the strong coupling regime of the very same system.
