混沌动力学
This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…
This paper revisits the send/retrieve message process using synchronization of the Lorenz system with a monochromatic message. We analyze how the fidelity of the retrieved signal depends on the message frequency and demonstrate message…
In this paper we present Chaoticus, a Python-based package for the GPU-accelerated integration of ODE systems and the computation of chaos indicators, including SALI, GALI, Lagrangian Descriptors based indicators and the Lyapunov exponent…
Unstable periodic orbits (UPOs) are believed to be the underlying dynamical structures of spatio-temporal chaos and turbulence. Finding these UPOs is however notoriously difficult. Matrix-free loop convergence algorithms deform entire…
Many parts of the Earth system are thought to have multiple stable equilibrium states, with the potential for rapid and sometimes catastrophic shifts between them. The most common frameworks for analyzing stability changes, however, require…
In general terms, intermittency is the property for which time evolving systems alternate among two or more different regimes. Predicting the instance when the regime switch will occur is extremely challenging, often practically impossible.…
We investigate the dynamical properties of cusp bifurcations in max-plus dynamical systems derived from continuous differential equations through the tropical discretization and the ultradiscrete limit. A general relationship between cusp…
The simplest case of a ring topology is numerically investigated using the Terahertz modeling. Numerical simulations demonstrate high level degree of complete synchronization. Some security implications for the Terahertz communication and…
The Kuramoto model, a paradigmatic framework for studying synchronization, exhibits a transition to collective oscillations only above a critical coupling strength in the thermodynamic limit. However, real-world systems are finite, and…
This study investigates how two- and three-wave configurations govern particle escape and transport in tokamak edge plasmas. Using a Hamiltonian model derived from drift-wave turbulence, we analyze test particle dynamics through Poincar\'e…
This paper shows that linearizing the transverse discontinuity mapping (TDM) in Filippov systems can produce inaccurate predictions of the dynamics in impact oscillators operating near a pre-stressed soft barrier. This discrepancy arises…
Shear-thickening fluids (STFs) become more viscous under shear stress, which makes them useful for many engineering and scientific applications. However, their behavior under normal forces, especially when these forces are applied…
Inferring control parameters in non-linear dynamical systems is an important task in analysing general dynamical behaviours, particularly in the presence of inherently deterministic chaos. Traditional approaches often rely on…
Since Lorenz's seminal work on a simplified weather model, the numerical analysis of nonlinear dynamical systems has become one of the main subjects of research in physics. Despite of that, there remains a need for accessible, efficient,…
Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control…
GRHT map refers to a planar map which showcases the coexistence of infinitely many stable periodic orbits via the phenomenon of Globally Resonant Homoclinic Tangencies. This paper investigates the geometric properties of coexistence regions…
This study examines anomalous diffusion and dynamical phase transitions in a nonlinear bouncer model with short-range interactions leading to velocity-dependent (adiabatic) collisions. By varying a control parameter, transitions between…
Several continuous dynamical systems have recently been proposed as special-purpose analog computers designed to solve combinatorial optimization problems such as $k$-SAT or the Ising problem. While combinatorial optimization problems are…
Periodic signals propagating along chains are common in biology, for example in locomotion and peristalsis, and are also of interest for continuum robots. In previous work we constructed such networks as 'feedforward lifts' of a central…
Discrete Lorenz attractors can be found in three-dimensional discrete maps. Discrete Lorenz attractors have similar topology to that of the continuous Lorenz attractor exhibited by the well studied 3D Lorenz system. However, the routes to…