Related papers: A simple method to enlarge a basin of attraction u…
This paper investigates and analyzes the dynamics of the two-dimensional Duffing map. Multistability behavior has been observed from the system numerically. Such behavior, especially the coexistence of chaotic and periodic attractors, is…
Chaotic bursting behaviors have been observed by many authors in neural dynamics mainly in the transition between different kinds of bursting behavior. As a well-known three-dimensional ODEs model with various bursting solutions, the…
The chaotic hypothesis discussed in [GC1] is tested experimentally in a simple conduction model. Besides a confirmation of the hypothesis predictions the results suggest the validity of the hypothesis in the much wider context in which, as…
In this paper, we investigate the precise behavior of orbits inside attracting basins. Let $f$ be a holomorphic polynomial of degree $m\geq2$ in $\mathbb{C}$, $\mathcal {A}(p)$ be the basin of attraction of an attracting fixed point $p$ of…
We show how random feature maps can be used to forecast dynamical systems with excellent forecasting skill. We consider the tanh activation function and judiciously choose the internal weights in a data-driven manner such that the resulting…
We made the chaotic circuit proposed by Chua and the memristic circuit proposed by Muthuswamy and Chua, and analyzed the behavior of the voltage of the capacitor, electric current in the inductor and the voltage of the memristor by adding…
Hamiltonian dynamics can be used to produce distant proposals for the Metropolis algorithm, thereby avoiding the slow exploration of the state space that results from the diffusive behaviour of simple random-walk proposals. Though…
This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the…
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…
The theory of stochastic resetting asserts that restarting a stochastic process can expedite its completion. In this paper, we study the escape process of a Brownian particle in an open Hamiltonian system that suffers noise-enhanced…
We present a method for generating robust chaos. It is based on the search algorithm weak symmetry violation in the reconstructed attractor. On its basis the smooth functions in the form of a system of finite-difference equations. To ensure…
We prove the stability of the critical hypersurfaces associated with the three-dimensional general relativistic Poynting-Robertson effect. The equatorial ring configures to be as a stable attractor and the whole critical hypersurface as a…
In 1976, Leon Chua showed that a thermistor can be modeled as a memristive device. Starting from this statement we designed a circuit that has four circuit elements: a linear passive inductor, a linear passive capacitor, a nonlinear…
The basin entropy is a measure that quantifies, in a system that has two or more attractors, the predictability of a final state, as a function of the initial conditions. While the basin entropy has been demonstrated on a variety of…
In this paper, we investigate the dynamical behavior of non-autonomous Lame thermoelastic systems within $N$-dimensional materials. With appropriate constraints on nonlinear characteristics and functional parameters, we initially establish…
Due to errors of numerical methods, qualitative behavior of the numerically simulated solution may be completely different from qualitative behavior of the real trajectory. Therefor in study of attractors the more useful idea is to simulate…
Aiming to provide a new class of game dynamics with good long-term rationality properties, we derive a second-order inertial system that builds on the widely studied "heavy ball with friction" optimization method. By exploiting a well-known…
An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal…
In this study, we investigate the effect of reservoir computing training data on the reconstruction of chaotic dynamics. Our findings indicate that a training time series comprising a few periodic orbits of low periods can successfully…
This paper presents a simple method to boost the robustness of quadrotors in trajectory tracking. The presented method features a high-gain disturbance observer (HGDO) that provides disturbance estimates in real-time. The estimates are then…