混沌动力学
Recent studies have shown that chaotic maps are well-suited for applications requiring unpredictable behaviour, making them a valuable tool for enhancing unpredictability and complexity. A method is developed using 3D parametric equations…
This work presents some results regarding three-dimensional billiards having a non-constant potential of Keplerian type inside a regular domain $D\subset \mathcal R^3$. Two models will be analysed: in the first one, only an inner Keplerian…
This study explores the integration of a diffusion control parameter into the chaotic dynamics of a modified bouncing ball model. By extending beyond simple elastic collisions, the model introduces elements that affect the diffusive…
Chimera states and bump states are collective synchronization phenomena observed independently (at different parameter regions) in networks of coupled nonlinear oscillators. And while chimera states are characterized by coexistence of…
By extending the extreme learning machine by additional control inputs, we achieved almost complete reproduction of bifurcation structures of dynamical systems. The learning ability of the proposed neural network system is striking in that…
This letter proposes using intermittent chaotic clocks, generated from chaotic maps, to drive cryptographic chips running the Advanced Encryption Standard as a countermeasure against Correlation Power Analysis attacks. Five different…
The Mackey-Glass system is a paradigmatic example of a delayed model whose dynamics is particularly complex due to, among other factors, its multistability involving the coexistence of many periodic and chaotic attractors. The prediction of…
In this paper, we study the generation and propagation of oscillatory solutions observed in the widely used Lorenz 96 (L96) systems. First, period-two oscillations between adjacent grid points are found in the leading-order expansions of…
A cantilever beam under axial flow, confined or not, is known to develop self-sustained oscillations at sufficiently large flow velocities. In recent decades, the analysis of this archetypal system has been mostly pursued under linearized…
Populations of coupled oscillators can exhibit a wide range of complex dynamical behavior, from complete synchronization to chimera and chaotic states. We can thus expect complex dynamics to arise in networks of such populations. Here we…
The Maslov index of a periodic orbit is an important piece in the semiclassical quantization of non-integrable systems, while almost all existing techniques that lead to a rigorous calculation of this index are elaborate and mathematically…
During the COVID-19 pandemic, it became evident that the effectiveness of applying intervention measures is significantly influenced by societal acceptance, which, in turn, is affected by the processes of opinion formation. This article…
The current study formulates a convective model of the Lorenz type near the temperature of maximum density. The existence of this temperature actualizes water dynamics in temperate lakes. There is a conceptual interest what this feature…
Although granular materials are the second most processed in industry after water, the theoretical study of granules-structure interactions is not as advanced as that of fluid-structure interactions due to the lack of a unified view of the…
This paper is dedicated to clarifying and introducing the correct application of Melnikov method in fractional dynamics. Attention to the complex dynamics of hyperbolic orbits and to fractional calculus can be, respectively, traced back to…
We explore the chaotic dynamics of a large one-dimensional lattice of coupled maps with diffusive coupling of varying strength using the covariant Lyapunov vectors (CLVs). Using a lattice of diffusively coupled quadratic maps we quantify…
The complex dynamics of baker's map and its variants in an infinite-precision mathematical domain have been extensively analyzed in the past five decades. However, their real structure implemented in a finite-precision computer remains…
In this work, we investigate the period doubling phenomenon in the periodically forced asymmetric Duffing oscillator. We use the known steady-state asymptotic solution -- the amplitude-frequency implicit function -- and known criterion for…
With the recent implementation of the Artemis Accords, interest in the cis-lunar space is rapidly increasing, necessitating the development of more precise and accurate modeling tools. While general-purpose mission design tools are…
We use the Toda chain model to demonstrate that numerical simulation of integrable Hamiltonian dynamics using time discretization destroys integrability and induces dynamical chaos. Specifically, we integrate this model with various…