混沌动力学
We perform analytical and quantitative analysis of the motion of a non-integrable pendulum with two degrees of freedom, in which an integrable nonlinear pendulum and a harmonic oscillator are weakly coupled through a non-integrable…
We investigate the effect of a constant static bias force on the dynamically induced shape morphing of a pre-buckled bistable beam, focusing on the beam's ability to change its vibration to be near different stable states under harmonic…
Transport is an important function of networks. Studying transport efficiency sheds light on the dynamic processes occurring within various underlying structures and offers a wide range of applications. To construct networks with different…
Regularization is a technique to improve generalization of machine learning (ML) models. A common form of regularization in the ML literature is to train on data where similar inputs map to different outputs. This improves generalization by…
The main properties of a dynamical system can be analyzed by examining the corresponding basins, either attraction basins in dissipative systems or escape basins in open Hamiltonian systems and area-preserving maps. In the latter case, the…
The primary focus of this thesis is the numerical investigation of chaos in Hamiltonian models describing charged particle orbits in plasma, star motions in barred galaxies, and orbits' diffusion in multidimensional maps. We systematically…
A close relation has recently emerged between two of the most fundamental concepts in physics and mathematics: chaos and supersymmetry. In striking contrast to the semantics of the word 'chaos,' the true physical essence of this phenomenon…
When placed in parallel magnetic and electric fields, the electron trajectories of a classical hydrogen atom are chaotic. The classical escape rate of such a system can be computed with classical trajectory Monte Carlo techniques, but these…
We consider the spectral transfers of sign-definite invariants in general wave turbulence systems equipped with a wave kinetic equation. We develop a formalism to investigate and to characterize these transfers, based on the ability to…
The Duffing oscillator describes the dynamics of a mass suspended on a spring with position-dependent stiffness. The mass is assumed to experience a linear damping and a time-dependent external forcing. The model has been instrumental in…
Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior,…
We calculate the maximum Lyapunov exponent of the motion in the separatrix map's chaotic layer, along with calculation of its width, as functions of the adiabaticity parameter $\lambda$. The separatrix map is set in natural variables; and…
Generalized synchronization (GS) describes a state in which two coupled dynamical systems exhibit a functional relationship between their variables. GS can be achieved by appropriately designing the coupling to constrain the dynamics onto…
The regular logistic map was introduced in 1960s, served as an example of a complex system, and was used as an instrument to demonstrate and investigate the period doubling cascade of bifurcations scenario of transition to chaos. In this…
From the integer quantum Hall effect, to swimming at low Reynolds number, geometric phases arise in the description of many different physical systems. In many of these systems the temporal evolution prescribed by the geometric phase can be…
This work explores the relationship between state space methods and Koopman operator-based methods for predicting the time-evolution of nonlinear dynamical systems. We demonstrate that extended dynamic mode decomposition with dictionary…
We investigate the role of inertia in the asynchronous state of a disordered Kuramoto model. We extend an iterative simulation scheme to the case of the Kuramoto model with inertia in order to determine the self-consistent fluctuation…
Josephson junctions (JJs) are by nature neuromorphic hardware devices capable of mimicking excitability and spiking dynamics. When coupled together or combined with other superconducting elements, they can emulate additional behaviors found…
Small, forested catchments are prototypes of terrestrial ecosystems and have been studied in several disciplines of environmental sciences since several decades. Time series of water and matter fluxes and nutrient concentrations from these…
The wave kinetic equation has become an important tool in different fields of physics. In particular, for surface gravity waves, it is the backbone of wave forecasting models. Its derivation is based on the Hamiltonian dynamics of surface…