混沌动力学
We introduce a constructive framework to learn effective Langevin equations from stationary time series. Unlike conventional approaches that require iterative calibration to match target statistics, our construction guarantees the observed…
Bifurcations in dynamical systems are often studied experimentally and numerically using a slow parameter sweep. Focusing on the cases of period-doubling and pitchfork bifurcations in maps, we show that the adiabatic approximation always…
We present a novel, model-free, and data-driven methodology for controlling complex dynamical systems into previously unseen target states, including those with significantly different and complex dynamics. Leveraging a parameter-aware…
Reservoir Computing (RC), a type of recurrent random neural network, is a powerful framework for modeling complex and chaotic dynamics. However, its autonomous (closed-loop) operation is often plagued by inherent instability. Moreover,…
Mean-field systems provide a natural framework in which collective effects persist as the number of degrees of freedom N increases, raising fundamental questions about the emergence of integrability and the nature of chaos in large but…
Chaos in both dissipative systems and conservative systems is investigated on the approach of renormalization group. It is found that the chaos is regarded as the critical phenomenon of equilibrium statistics in phase space. The two…
We study large but finite neural networks that, in the thermodynamic limit, admit an exact low-dimensional mean-field description. We assume that the governing mean-field equations describing macroscopic quantities such as the mean firing…
We study the bifurcation scenario of a three-degree-of-freedom Hamiltonian system, a model based on the Lagrange restricted 3-body problem: a test particle moving in the gravitational field of a pair of interacting dwarf galaxies. The phase…
In this paper we demonstrate that the phase space arclength of a trajectory, quantified by the time-averaged Lagrangian descriptor, is a robust and self-contained chaos indicator. By invoking Birkhoff's Ergodic Partition Theorem, we show…
Mechanical lattices support topological wave phenomena governed by geometric phases. We develop a compact Hilbert space description for one-dimensional elastic chains, expressing intra-cell motion as a normalized superposition of orthogonal…
We introduce the $\alpha$-Gauss-Logistic map, a new nonlinear dynamics constructed by composing the logistic and $\alpha$-Gauss maps. Explicitly, our model is given by $x_{t+1} = f_L(x_t)x_t^{-\alpha} - \lfloor f_L(x_t)x_t^{-\alpha} \rfloor…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
The scope of the paper is the analysis of the impact of flow reversal on the dynamics of cascades of reactors. Periodic and chaotic oscillations occur in the analyzed system. There is a dependence between the oscillation period of the state…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
Three kinds of fractal solutions of model of reactors are presented. The first kind concerns the structure of Feigenbaum_s diagram on the limit of chaos. The second kind and the third one concern the effect of initial conditions on the…
The present study deals with a theoretical analysis of the effect of delay time of energy transport upon the generation of complex dynamics in continuous physical system. The importance of this time for the presence of quasi - periodicity…
The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have real rational number values. Applicable characteristic…
To stabilize the periodic operation of a chemical reactor the oscillation period should be determined precisely in real time. The method discussed in the paper is based on adaptive sampling of the state variable with the use of chaotic…
The correlation diagrams of vibrational energy levels considering the Planck constant as a variable parameter have proven as a very useful tool to study vibrational molecular states, and more specifically in relation to the quantum…
Walking droplets are millimetric fluid drops that propel themselves across a vibrated liquid bath through interaction with their self-generated waves. They constitute classical active wave-particle entities and exhibit a range of…