Chaos In Dynamical Systems

By A. Klug. 2016

1,593 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0800f8b1f48b6e09525270ddbfeb2ad550e3e97f

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Citations in the corpus

Statistical models for spatial patterns of heavy particles in turbulence (2014, background): “In d spatial dimensions, there are d such exponents [108], describing the long-term dynamics of spatial separations between a test particle and particles in its vicinity.”
Explosions of chaotic sets (2000, background): “For an introduction to crises and metamorphoses we refer the reader to [36,37].”
WKB theory of large deviations in stochastic populations (2016, background): “Two main types of noise have been identified: intrinsic, or demographic noise and extrinsic, or environmental noise.”
Complex dynamic behaviors of a discrete-time predator-prey system (2017, methodology): “Numerical simulations, including bifurcation diagrams, phase portraits, maximum Lyapunov exponents and fractal dimension [1, 2, 16, 24], are used to verify the theoretical analysis and to display new and interesting dynamical behaviors of the system (1.”
Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems (2016, background): “(50) is effectively a three-dimensional dynamical system, in which chaos can arise [155].”
Acceleration of the charged particles due to chaotic scattering in the combined black hole gravitational field and asymptotically uniform magnetic field (2015, methodology): “We can examine the efficiency of the charged particle acceleration process for the whole set of initial conditions using the chaotic scattering theory as it is presented in chapter 5 of [49] and chapter 8 of [50].”
Many-body chaos and energy dynamics in holography (2018, background): “At the classical level, chaos is believed to provide the microscopic dynamical mechanism for macroscopic phenomena such as transport and thermalisation (for example see [21, 22]).”
Intrinsic dimension estimation: Advances and open problems (2016, methodology): “Grassberger–Procaccia algorithm A good alternative to the Box-Counting Dimension, among many proposed [74,101] is the Correlation Dimension [35], defined as follows.”
Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics (2015, background): “However, Nonnenmacher and Schenk (2008) demonstrated that a damped quantum map used as a toy model for dielectric cavities shows the conventional Weyl law. While the Weyl law characterizes the smooth part of the density of states, the statistical analysis of the energy levels addresses the fluctuati”
A lower bound error for free-run simulation of the polynomial NARMAX (2016, background): “Numerous researchers are confident in subscribing a chaotic behaviour to various systems through numerical solutions (Ott, 2002).”
Low-dimensional dynamics of populations of pulse-coupled oscillators (2013, background): “Chimeras exist between the dashed line (the locus of a saddle-node bifurcation of limit cycles) and the solid line (corresponding to both the boundary crisis [46,47] and the saddle-node bifurcation of cycles).”