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Dynamical Systems Theory [PDF]
The International Journal of Communication and Linguistic Studies, 2003 This chapter introduces the basic concepts of dynamical systems theory, and several basic mathematical methods for controlling chaos. The main goal of this chapter is to provide an introduction to and a summary to the theory of dynamical systems with particular emphasis on fractal theory, chaos theory, and chaos control.
Oscar Castillo, Patricia Melín
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Dynamical systems theory of cellular reprogramming
Physical Review Research, 2022 In cellular reprogramming, almost all epigenetic memories of differentiated cells are erased by the overexpression of a few genes, resulting in regaining pluripotency, the potential for differentiation.
Yuuki Matsushita +2 more
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Vector dissipativity theory for discrete-time large-scale nonlinear dynamical systems [PDF]
Advances in Difference Equations, 2004 In analyzing large-scale systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solution properties of the large-scale system are then deduced from the solution properties of the individual subsystems and
Wassim M. Haddad +3 more
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A Case Study of Combined Application of Smart Materials in a Thermal Energy Harvester with Vibrating Action [PDF]
Journal of Applied and Computational Mechanics, 2021 This paper demonstrates a case study of a combined application of smart materials in a thermal energy harvester with vibrating action. The conceptual design of the harvester is based on a Shape Memory Alloy wire attached to the free end of a ...
Rosen Mitrev +4 more
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Category of Discrete Dynamical System
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 A dynamical system is a method that can describe the process, behavior, and complexity of a system. In general, a dynamical system consists of a discrete dynamical system and a continuous dynamical system.
Ananda Ayu Permatasari +2 more
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Dynamical systems theory for music dynamics [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1995 We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of temporal dynamics in music. (i) Phase space portraits are constructed from the time series wherefrom the dimensionality is evaluated as a measure of the global dynamics of each ...
Boon, Jean-Pierre, Decroly, O.
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Learning Theory for Dynamical Systems
SIAM Journal on Applied Dynamical Systems, 2023 The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then explicitly learning the dynamics from this information.
Tyrus Berry, Suddhasattwa Das
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Mathematics, 2021 This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton–Jacobi theory. The relation with the “classical” Hamiltonian approach using canonical transformations is also analyzed ...
Narciso Román-Roy
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Physical Review Research, 2022 Dimension reduction techniques for dynamical systems on networks are considered to promote our understanding of the original high-dimensional dynamics.
Naoki Masuda, Prosenjit Kundu
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Time-averaging axion-like interacting scalar fields models
European Physical Journal C: Particles and Fields, 2021 In this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields $$\phi _1$$ ϕ 1 and $$\phi _2$$ ϕ 2 interacting through a term added to its potential. Introducing novel dynamical variables, and a dimensionless
Saikat Chakraborty +3 more
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