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Spin systems with hyperbolic symmetry originated as simplified models for the Anderson metal--insulator transition, and were subsequently found to exactly describe probabilistic models of linearly reinforced walks and random forests. In…

Probability · Mathematics 2024-07-11 Roland Bauerschmidt , Tyler Helmuth

In this paper, is used the Lagrangian classical mechanics for modeling the dynamics of an underactuated system, specifically a rotary inverted pendulum that will have two equations of motion. A basic design of the system is proposed in…

Robotics · Computer Science 2017-06-19 Juan Libardo Duarte Madrid , P. A. Ospina-Henao , E González Querubín

A six-dimensional Rossler-Lorenz hybrid has two coexistent attractors. Both, either or neither may be strange.

Chaotic Dynamics · Physics 2007-05-23 R. C. Johnson

A two-fluid model is derived from the plasma kinetic equations using the moment model reduction method. The moment method we adopt was recently developed with a globally hyperbolic regularization where the moment model attained is locally…

Plasma Physics · Physics 2020-05-14 Ruo Li , Yixiao Lu , Yanli Wang

An account is given of the features, of the kind pertaining to q-statistics, of the dynamics at the one-dimensional critical attractors associated to the three familiar routes to chaos, intermittency, period doubling and quasiperiodicity.…

Statistical Mechanics · Physics 2013-08-29 A. Robledo

This study presents a theoretical framework for planning and controlling agile bipedal locomotion based on robustly tracking a set of non-periodic apex states. Based on the prismatic inverted pendulum model, we formulate a hybrid…

Robotics · Computer Science 2015-11-17 Ye Zhao , Benito R. Fernandez , Luis Sentis

We experimentally explore solutions to a model Hamiltonian dynamical system derived in Colliander et al., 2012, to study frequency cascades in the cubic defocusing nonlinear Schr\"odinger equation on the torus. Our results include a…

Analysis of PDEs · Mathematics 2012-09-17 James E. Colliander , Jeremy L. Marzuola , Tadahiro Oh , Gideon Simpson

The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more dimensions than other regions. Imagine a situation where two…

Chaotic Dynamics · Physics 2018-11-14 Yoshitaka Saiki , Miguel A. F. Sanjuan , James A. Yorke

Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…

Chaotic Dynamics · Physics 2009-10-31 Tomaz Prosen , Thomas H. Seligman , Hans A. Weidenmueller

Extreme multistability (EM) is characterized by the emergence of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. EM implies complex and hardly predictable asymptotic dynamical behavior. We…

Adaptation and Self-Organizing Systems · Physics 2023-09-28 Zhen Su , Jürgen Kurths , Yaru Liu , Serhiy Yanchuk

Physical systems obey strict symmetry principles. We expect that machine learning methods that intrinsically respect these symmetries should have higher prediction accuracy and better generalization in prediction of physical dynamics. In…

Machine Learning · Computer Science 2021-11-02 Weichi Yao , Kate Storey-Fisher , David W. Hogg , Soledad Villar

Multi-wing chaotic attractors are highly complex nonlinear dynamical systems with higher number of index-2 equilibrium points. Due to the presence of several equilibrium points, randomness of the state time series for these multi-wing…

Chaotic Dynamics · Physics 2013-01-03 Anish Acharya , Saptarshi Das , Indranil Pan

A synthetic fluid dynamo built in the spirit of the Bullard device [E. C. Bullard, Proc. Camb. Phil. Soc., 51, 744 (1955)] is investigated. It is a two-step dynamo in which one process stems from the fluid turbulence, while the other part…

This paper considers a nonlinear spherical pendulum whose suspension point performs high-frequency spatial vibrations. The dynamics of this pendulum can be described by averaging its Hamiltonian over phases of vibrations. Rotationally…

General Mathematics · Mathematics 2025-09-12 Yan Luo , Kaicheng Sheng

Kicked double-well system is investigated both analytically and numerically. Phenomenological formula for ground quasienergy splitting is obtained using resonances overlap criterion in the framework of chaotic instanton approach. Results of…

Chaotic Dynamics · Physics 2008-01-15 V. I. Kuvshinov , A. V. Kuzmin , V. A. Piatrou

In this paper we study a two-parameter family of planar maps characterized by two distinct invariant subspaces. The model reveals the existence of two chaotic attractors within these subspaces. We identify parameter values at which these…

Chaotic Dynamics · Physics 2025-02-10 Fatemeh Helen Ghane , Marc Kesseböhmer

We describe a mechanism for transport of energy in a mechanical system consisting of a pendulum and a rotator subject to a random perturbation. The perturbation that we consider is the product of a Hamiltonian vector field and a scalar,…

Dynamical Systems · Mathematics 2024-09-06 Anna Maria Cherubini , Marian Gidea

This letter suggests a new way to investigate 3-D chaos in spatial and frequency domains simultaneously. After spatially decomposing the Lorenz attractor into two separate scrolls with peaked spectra and a 1-D discrete-time zero-crossing…

Chaotic Dynamics · Physics 2016-08-16 Gonzalo Álvarez , Shujun Li , Jinhu Lü , Guanrong Chen

We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of…

Dynamical Systems · Mathematics 2014-12-22 Gabriel Fuhrmann , Maik Gröger , Tobias Jäger

An investigation of the mesoscopic dynamics of chemical systems whose mass action equation gives rise to a deterministic chaotic attractor is carried out. A reactive lattice-gas model for the three-variable autocatalator is used to provide…

chao-dyn · Physics 2009-10-28 Raymond Kapral , Xiao-Guang Wu