混沌动力学
The nonlinear Schr\"odinger equation (NLSE) underpins nonlinear wave phenomena in optics, Bose-Einstein condensates, and plasma physics, but computing its excited states remains challenging due to nonlinearity-induced non-orthonormality.…
The work concentrates on relations, which are general and model independent in chaotic system, between time averages of a few (typically {\it very few}) observables. Equilibrium thermodynamics provides a guide and here is attempted to argue…
Symbolic dynamics serves as a crucial tool in the study of chaotic systems, prompting extensive research into various methods for symbolic partitioning. The limitations of these methods are heuristic and empirical for the partition the…
Hybrid chaos synchronization between ring-line networks topologies is explored on the example of Ikeda modeling, famous multidisciplinary system. It is established that high quality complete synchronization between constituent lasers is a…
A complete analysis of classical periodic orbits (POs) and their bifurcations was conducted in spherical harmonic oscillator system with spin-orbit coupling. The motion of the spin is explicitly considered using the spin canonical variables…
We conduct numerical analysis of the 2-dimensional discrete-time gene expression model originally introduced by Andrecut and Kauffman (Phys. Lett. A 367: 281-287, 2007). In contrast to the previous studies, we analyze the dynamics with…
We investigate how nonlinear behaviour (both of forcing in time and of the system itself) can affect the skill of early warning signals to predict tipping in (directionally) coupled bistable systems when using measures based on critical…
In this paper, we discuss an example of current importance with a future perspective in engineering, in which excitation sources always have limited power, limited inertia, and their frequencies vary according to the instantaneous state of…
In this paper, we study the stability of a simple model of a Hyperloop vehicle resulting from the interaction between electromagnetic and aeroelastic forces for both constant and periodically varying coefficients (i.e., parametric…
Various phonemes are considered in terms of nonlinear dynamics. Phase portraits of the signals in the embedded space, correlation dimension estimate and the largest Lyapunov exponent are analyzed. It is shown that the speech signals have…
Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular…
The Chua's circuit is examined using a State Controlled-Cellular Neural Network (SC-CNN) framework with two logical square wave input signals. We illustrate, in particular, that this nonlinear circuit can generate all the basic logic…
This study analyses the dynamical consequences of heterogeneous temporal delays within a quorum sensing-inspired (QS-inspired) system, specifically addressing the differential response kinetics of two sub-populations to signalling…
We solve the fully-connected Ising model in the presence of dissipation and time-periodic field, with the corresponding Lindblad equation having a time-periodic Liouvillian. The dynamics of the magnetizations is studied by using both the…
Reservoir computing has proven effective for tasks such as time-series prediction, particularly in the context of chaotic systems. However, conventional reservoir computing frameworks often face challenges in achieving high prediction…
This paper presents a simple model for such processes as chaos spreading or turbulence spillover into stable regions. In this simple model the essential transport occurs via inelastic resonant interactions of waves on a lattice. The process…
Generating long-term trajectories of dissipative chaotic systems autoregressively is a highly challenging task. The inherent positive Lyapunov exponents amplify prediction errors over time. Many chaotic systems possess a crucial property -…
The interplay between chaos and thermalization in weakly non-integrable systems is a rich and complex subject. Interest in this area is further motivated by a desire to develop a unified picture of chaos for both quantum and classical…
A new machine learning scheme, termed versatile reservoir computing, is proposed for sustaining the dynamics of heterogeneous complex networks. We show that a single, small-scale reservoir computer trained on time series from a subset of…
The distribution of the consecutive level-spacing ratio is now widely used as a tool to distinguish integrable from chaotic quantum spectra, mostly due to its avoiding of the numerical spectral unfolding. Similar to the use of the…