The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled oscillators. In this paper, we study the emergence of chaos in chains of locally coupled identical pendulums with constant torque. The study of the scenarios of the emergence (disappearance) and properties of chaos is done as a result of changes in (i) the individual properties of elements due to the influence of dissipation in this problem and (ii) the properties of the entire ensemble under consideration, determined by the number of interacting elements and the strength of the connection between them. It is shown that an increase of dissipation in an ensemble with a fixed coupling force and a number of elements can lead to the appearance of chaos as a result of a cascade of period-doubling bifurcations of periodic rotational motions or as a result of invariant tori destruction bifurcations. Chaos and hyperchaos can occur in an ensemble by adding or excluding one or more elements. Moreover, chaos arises hard since in this case, the control parameter is discrete. The influence of the coupling strength on the occurrence of chaos is specific. The appearance of chaos occurs with small and intermediate coupling and is caused by the overlap of the existence of various out-of-phase rotational mode regions. The boundaries of these areas are determined analytically and confirmed in a numerical experiment. Chaotic regimes in the chain do not exist if the coupling strength is strong enough. The dimension of an observed hyperchaotic regime strongly depends on the number of coupled elements.
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http://dx.doi.org/10.1063/5.0044521 | DOI Listing |
Neural Netw
January 2025
Defense Innovation Institute, Chinese Academy of Military Science, Beijing 100071, China; Intelligent Game and Decision Laboratory, China.
The Physics-informed Neural Network (PINN) has been a popular method for solving partial differential equations (PDEs) due to its flexibility. However, PINN still faces challenges in characterizing spatio-temporal correlations when solving parametric PDEs due to network limitations. To address this issue, we propose a Physics-Informed Neural Implicit Flow (PINIF) framework, which enables a meshless low-rank representation of the parametric spatio-temporal field based on the expressiveness of the Neural Implicit Flow (NIF), enabling a meshless low-rank representation.
View Article and Find Full Text PDFHeliyon
January 2025
Unité de Recherche d'Automatique et d'Informatique Appliquée (UR-AIA), IUT-FV Bandjoun University of Dschang, P.O. Box 134, Bandjoun, Cameroon.
This study presents a family of coexisting multi-scroll chaos in a network of coupled non-oscillatory neurons. The dynamics of the system are analyzed using phase portraits, basins of attraction, time series, bifurcation diagrams, and spectra of Lyapunov exponents. The coexistence of multiple bifurcation diagrams leads to a complex pattern of multi-scroll formation, which is further complicated by the presence of coexisting single-scroll attractors that merge to form multi-scroll chaos.
View Article and Find Full Text PDFBioinspir Biomim
January 2025
Mathematics and Statistics, College of New Jersey, 2000 Pennington Road, Ewing, New Jersey, 08628, UNITED STATES.
Tomopterids are mesmerizing holopelagic swimmers. They use two modes of locomotion simultaneously: drag-based metachronal paddling and bodily undulation.has two rows of flexible legs (parapodia) positioned on opposite sides of its body.
View Article and Find Full Text PDFMethods
January 2025
National Center for Applied Mathematics in Hunan, Xiangtan University, Hunan 411105, China; Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Hunan 411105, China. Electronic address:
The subcellular localization of long non-coding RNAs (lncRNAs) is crucial for understanding the function of lncRNAs. Since the traditional biological experimental methods are time-consuming and some existing computational methods rely on high computing power, we are committed to finding a simple and easy-to-implement method to achieve more efficient prediction of the subcellular localization of lncRNAs. In this work, we proposed a model based on multi-source features and two-stage voting strategy for predicting the subcellular localization of lncRNAs (MVSLLnc).
View Article and Find Full Text PDFHeliyon
July 2024
Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj 8100, Bangladesh.
Qualitative analysis in mathematical modeling has become an important research area within the broad domain of nonlinear sciences. In the realm of qualitative analysis, the bifurcation method is one of the significant approaches for studying the structure of orbits in nonlinear dynamical systems. To apply the bifurcation method to the (2 + 1)-dimensional double-chain Deoxyribonucleic Acid system with beta derivative, the bifurcations of phase portraits and chaotic behaviors, combined with sensitivity and multi-stability analysis of this system, are examined.
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