Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering

By D. Lathrop. 2015

3,167 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d7db42b8ef68e84526922ae50420b062c2397dad

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Citations in the corpus

Classical discrete time crystals (2018, background): “Naively, given that the undamped equation (7) is the sine-Gordon representation of the Ising model, it might seem that period-doubling is analogous to the breaking of the internal Ising symmetry generated by ∼ ∼ θ θ → ±π, so that the destruction of the CDTC would occur through something like an Isin”
Transient phenomena in ecology (2018, background): “See (70, 71) for further elaboration of ideas from dynamical systems.”
Control Principles of Complex Networks (2015, background): “Chaotic behavior commonly emerges in natural and engineered systems, being encountered in chemistry, nonlinear optics, electronics, fluid dynamics, meteorology, and biology (Strogatz, 1994).”
Opening the Black Box: Low-Dimensional Dynamics in High-Dimensional Recurrent Neural Networks (2013, background): “The full analysis would therefore entail finding all candidate points of the RNN, linearizing the dynamics around each one, and finally trying to understand the interaction between different regions (Strogatz, 1994; Ott, 2002).”
Bifurcation analysis and chaos control in discrete-time glycolysis models (2018, background): “In other words, glycolysis is a biochemical reaction in living cells in which these cells obtain energy by utilization of glucose, and this biochemical process can be modeled through the following differential system [1,2]:”
Procedural content generation for games: A survey (2013, methodology): “Many systems used in games are similar to textbook complex systems and models [Alexander 1977; Strogatz 1994; Edelstein-Keshet 2005].”
An Overview of Assessment Methods for Synchronization Stability of Grid-Connected Converters Under Severe Symmetrical Grid Faults (2019, positive): “This is also known as the phase-plane analysis or phase portrait of the problem which has a unique solution given that f is continuously differentiable [50].”
Mental disorders as networks of problems: a review of recent insights (2016, positive): “Specifically, transitions are preceded by a phenomenon referred to as critical slowing down [29, 32, 33], which means that it takes longer for a system to recover from perturbations.”
The anticipating brain is not a scientist: the free-energy principle from an ecological-enactive perspective (2016, background): “Such synchronization is a general and common phenomenon in non-linear dynamics (Strogatz 1994).”
Musical creativity and the embodied mind (2018, methodology): “…While this approach has been used to offer useful mathematical descriptions of a range of non-organic self-organizing systems (Clark, 2001; Strogatz, 1994, 2001), it has also been explored more recently in biological contexts associated with coordinated movement, communication, problem…”
Early warning signals also precede non-catastrophic transitions (2013, background): “This implies that slowing-down is also to be expected (Strogatz 1994, Kuehn 2011, Lim and Epueranu 2011, Thompson and Sieber 2011).”
A Memristor-Based Hyperchaotic System with Hidden Attractors: Dynamics, Synchronization and Circuital Emulating (2015, background): “…applied in various areas, such as secure communications, random generators, signal processing, pattern formation of modelling of complex systems [6-12], studies on memristor [13-21] have only received significant attention recently after the realization of a solid-state thin film two-terminal…”
NAIS-Net: Stable Deep Networks from Non-Autonomous Differential Equations (2018, background): “theory, this property is central to stability analysis which investigates the properties of dynamical systems under which they converge to a single steady state without exhibiting chaos [25, 42, 39].”
Learning Dynamics and Heterogeneity of Spatial-Temporal Graph Data for Traffic Forecasting (2021, background): “Generally speaking, the concept dynamics is usually associated with a physical quantity that changes over time, and the dynamics describes how the quantity evolves in time [13].”
Attractor and integrator networks in the brain (2021, background): “1f), or chaotic (dynamics that are inherently unpredictable due to high sensitivity to small changes in the state [27]).”
Design-Oriented Transient Stability Analysis of PLL-Synchronized Voltage-Source Converters (2018, positive): “As for the second-order nonlinear dynamic system, the phase portrait approach provides an intuitive and design-oriented analysis [28], [29].”