混沌动力学
In this work, we quantify the time scales and information flow associated with multiscale energy transfer in a weakly turbulent system. This is done through a greedy optimization algorithm which finds the maximum conditional-mutual…
The well-known 1089 trick reflects an amazing trait of digital reversal process and reminisces of a limiting attractor in dynamical systems even though it takes only two steps. It is natural to consider the situations when the number of…
Synchronization transition in oscillatory networks manifests itself as the appearance of a periodic global mode. While perfect in the thermodynamic limit, this mode fluctuates for finite ensembles. We characterize the coherence of this mode…
We examine the differences between the driven turbulence described by the Kuramoto-Sivashinsky (KS) equation and the second law of thermodynamics. A general velocity and entropy density system is analyzed with the unified thermodynamic…
Restarting a stochastic search process can accelerate its completion by providing an opportunity to take a more favorable path with each reset. This strategy, known as stochastic resetting, is well studied in random processes. Here, we…
Stochastic resonance (SR) manifests as switching dynamics between two quasi-stationary states in the stochastic Mackey-Glass equation. We identify chaotic SR, arising from the coexistence of resonance and chaos in stochastic dynamics. In…
Machine learning methods have shown promise in learning chaotic dynamical systems, enabling model-free short-term prediction and attractor reconstruction. However, when applied to large-scale, spatiotemporally chaotic systems, purely…
A number of simple chaotic three-dimensional dynamical systems (DSs) with quadratic polynomials on the right-hand sides are reported in the literature, containing exactly 5 or 6 monomials of which only 1 or 2 are quadratic. However, none of…
Synchronization of self-sustained oscillators under fixed-frequency and amplitude forcing is well understood, but how time-varying forcing mangles phase locking has been much less explored. Theory predicts that slow, deterministic…
A hard-wall billiard is a mathematical model describing the confinement of a free particle that collides specularly and instantaneously with boundaries and discontinuities. Soft billiards are a generalization that includes a smooth boundary…
Unstable periodic orbits (UPOs) are the non-chaotic, dynamical building blocks of spatio-temporal chaos, motivating a first-principles based theory for turbulence ever since the discovery of deterministic chaos. Despite their key role in…
How higher-order interactions influence dynamical behavior in networks of coupled chaotic oscillators remains an open question. To address this, we investigate emergent dynamical behaviors in a wheel network of R\"ossler and Lorenz…
Recurrence quantification analysis (RQA) is a widely used tool for studying complex dynamical systems, but its standard implementation requires computationally expensive calculations of recurrence plots (RPs) and line length histograms.…
Atmospheric Rivers (ARs) are filamentary moisture pathways responsible for a large fraction of extreme precipitation and often occur as interacting filament bundles within the same synoptic regime. Existing diagnostics typically analyze ARs…
Synchronization control in networked dynamical systems requires regulating not only whether coherence is achieved, but also when and to what extent it emerges. We propose a physics-informed neural network (PINN) framework for…
The concept of transcripts was introduced in 2009 as a means to characterize various aspects of the functional relationship between time series of interacting systems. Based on this concept that utilizes algebraic relations between ordinal…
We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition…
In 1962, astronomers Michel H\'enon and Carl Heiles studied orbits of stars around centers of galaxies to determine the third integral of motion in galactic dynamics. In order to do this, they reduced the system down to a 2-dimensional…
Classical chaos theory rests on the notion of universality, whereby disparate dynamical systems share identical scaling laws. Existing universality classes, however, implicitly assume Markovian dynamics. Here, a logistic map endowed with…
Coarse-graining a chaotic bistable oscillator into a binary symbol sequence is a standard reduction, but it often obscures the geometry of the reduced state space and structural constraints of physically meaningful stochastic evolution. We…