混沌动力学
We investigate phase-locked solutions of a continuum field of nonlocally coupled identical phase oscillators with distance-dependent propagation delays. Equilibrium relations for both synchronous and traveling wave solutions in the…
When parameters of a dynamical system change sufficiently fast, critical transitions can take place even in the absence of bifurcations. This phenomenon is known as rate-induced tipping and has been reported in a variety of systems, from…
Tipping behavior can occur when an equilibrium of a dynamical system loses stability in response to a slowly varying parameter crossing a bifurcation threshold, or where noise drives a system from one attractor to another, or some…
In bistable dynamical systems driven by Wiener processes, the widely used Kramers' law relates the strength of the noise forcing to the average time it takes to see a noise-induced transition from one attractor to the other. We extend this…
In finite-size systems undergoing a continuous phase transition, the passage from the symmetric phase to the broken-symmetry phase is accomplished through a hysteresis zone, up to spontaneous symmetry breaking (SSB). In the present work, we…
We consider a formal (approximate) integral of motion in Hamiltonians of the form $H=\frac{1}{2}(X^2+Y^2+\omega_1^2x^2+\omega_2^2y^2)+\epsilon(\eta xy^2+\alpha x^3+\beta x^2y+\gamma y^3)$ generalizing previous cases with $\beta=\gamma=0$.…
We study the escape of particles in the lemon billiard, a two-parameter family of billiard systems defined by the intersection of two identical circles. Using numerical simulations, we explore how the survival probability depends on the…
The Rulkov model, which simulates the behavior of biological neurons, is modified by replacing one of its control parameters with a memristive, sigmoid-type function of finite memory. This modification causes the parameter to vary according…
Twin-wire laser directed energy deposition (TW-LDED) provides a promising route for alloying and fabrication of compositionally graded structures. However, inherent multiparameter coupling in twin-wire systems critically exacerbates both…
A shell model can be considered as a chain of triads, where each triad can be interpreted as a nonlinear oscillator that can be mapped to a spinning top. Investigating the relation between phase dynamics and intermittency in a such a chain…
We demonstrate that the conformal-map method introduced by Robnik in 1984 for nonrelativistic quantum billiards is not applicable for the quantization of relativistic neutrino billiards (NBs) consisting of a massless non-interacting…
We report on the experimental study of the spectral properties of quantum systems consisting of two quantum billiards (QBs), one with chaotic, the other one with integrable classical dynamics, that are coupled to each other via an opening…
Recent theoretical developments of reservoir computing have clarified a sufficient condition about which reservoir computing can capture the dynamics of a target system, enabling the reconstruction of dynamical invariants. Even when the…
The real-time prediction of chaotic systems requires a nonlinear-reduced order model (ROM) to forecast the dynamics, and a stream of data from sensors to update the ROM. Data-driven ROMs are typically built with a two-step strategy: data…
In the present work we describe a way to assess memory capability of real devices, while proposing to the engineering community what to pursue to create devices with deep associated memory capability. The study of the signal produced by a…
Recurrence Quantification Analysis (RQA) is a widely used method for capturing the dynamical structure embedded in time series data, relying on the analysis of recurrence patterns in the reconstructed phase space via recurrence plots (RPs).…
In this paper we introduce a chaos indicator derivable from Lagrangian descriptors (LDs), defined as the difference in LD values between two neighboring trajectories. This difference LD is remarkably easy to implement and interpret,…
Recurrence plots (RPs) are powerful tools for visualizing time series dynamics; however, traditional Recurrence Quantification Analysis (RQA) often relies on global metrics, such as line counting, that can overlook system-specific,…
The dynamics of nonlinear oscillators are investigated. We study the formation of $1:2$ resonance in nonlinear periodically forced oscillators due to period doubling of the primary $1:1$ resonance, or born independently. We compute the…
We introduce the one-dimensional Morse-soft-Coulomb (MsC) potential consisting of a Morse repulsive barrier smoothly connected with a soft-core Coulomb potential at the origin. This new potential has a single parameter that controls the…