New Approach to Multiplicative Stochastic Processes. II

Maximum likelihood estimators for generalized Cauchy processes

“…25 Various simple models which generate intermittent chaos ͑types I, II, and III͒ by chaotic modulation have been studied. 23 However, the related inverse problems for inferring parameters of models with various intermittent nature only from time series data are quite laborious, in general. The intermittent natures in more sophisticated models are not well described both physically and mathematically.…”

“…It has been used to characterize the features of temporal correlation in time series and of structure of attractors in the phase space in complex chaotic/turbulent time series analysis. [23][24][25][26][27] On the other hand, Tsallis et al 14 proposed a new theory of q-entropy to derive a power-law-type distribution. Their studies on the q-averaging method help us to avoid mathematical divergence of the variance.…”

Amplitude-Phase Synchronization at the Onset of Permanent Spatiotemporal Chaos

“…The postcrisis dynamical system has the ability to keep the memory of its precrisis structures, as evidenced in the postcrisis STCA wherein the phase-space structure of the precrisis sheetlike TCA can still be recognized, which corresponds to TCS of Fig. 2 [13] at the transition from TCA to STCA, and an inverse blowout bifurcation at the transition from STCA to TCA. Prior to the blowout bifurcation, trajectories of TCA are confined to a synchronization manifold represented by the sheetlike structure of Fig.…”

Synchronization of coupled chaotic dynamics on networks

“…Exact synchronization corresponds to the situation where the dynamical variables have identical values, i.e. two dynamical variables x i and x j are exactly synchronized if x i (t) = x j (t) [16]. …”