Search results for "phase space methods"
showing 3 items of 3 documents
Approximating hidden chaotic attractors via parameter switching.
2018
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …
Unraveling the nature of universal dynamics in O(N) theories
2020
Many-body quantum systems far from equilibrium can exhibit universal scaling dynamics which defy standard classification schemes. Here, we disentangle the dominant excitations in the universal dynamics of highly occupied N-component scalar systems using unequal-time correlators. While previous equal-time studies have conjectured the infrared properties to be universal for all N, we clearly identify for the first time two fundamentally different phenomena relevant at different N. We find all N >= 3 to be indeed dominated by the same Lorentzian "large-N" peak, whereas N = 1 is characterized instead by a non-Lorentzian peak with different properties, and for N = 2, we see a mixture of two cont…
Inferring directionality of coupled dynamical systems using Gaussian process priors: Application on neurovascular systems
2022
Dynamical system theory has recently shown promise for uncovering causality and directionality in complex systems, particularly using the method of convergent cross mapping (CCM). In spite of its success in the literature, the presence of process noise raises concern about CCM's ability to uncover coupling direction. Furthermore, CCM's capacity to detect indirect causal links may be challenged in simulated unidrectionally coupled Rossler-Lorenz systems. To overcome these limitations, we propose a method that places a Gaussian process prior on a cross mapping function (named GP-CCM) to impose constraints on local state space neighborhood comparisons. Bayesian posterior likelihood and…