Nonlinear Dynamics and Chaos

By B. Kendall. 2001

2,944 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f6931a0bf786bc5bb20bbd4d94e6e5c85c452023

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Economics and Econometrics

In Statistical and Nonlinear Physics

Citations in the corpus

Feedback Systems: An Introduction for Scientists and Engineers (2008, neutral): “A very readable introduction to dynamical systems is given by Strogatz [Sto94].”
Complex dynamic behaviors of a discrete-time predator–prey system (2007, background): “2), period-doubling phenomenon and the onset of chaos in the sense of Li–Yorke [6] occur for some values of r0 [7,8].”
Large-amplitude non-linear normal modes of piecewise linear systems (2004, background): “Due to their practical importance, the dynamic behavior of piecewise linear systems has been the subject of many investigations, which mainly focus on forced response under periodic excitation [19–21], including dynamic behaviors such as bifurcations and chaos [22–24].”
Evolutionary game theory: Theoretical concepts and applications to microbial communities (2010, background): “This section is intended to give a concise introduction into elementary concepts of nonlinear dynamics [12].”
Learning CPG-based biped locomotion with a policy gradient method (2005, methodology): “In this section, we analyze linear stability of a periodic orbit in learned biped walking around a fixed point using a return map [22].”
Symbolic dynamic analysis of complex systems for anomaly detection (2004, methodology): “The apparatus implements a second-order non-autonomous, forced Du7ng equation in real time [23].”
Quantum-Inspired Particle Swarm Optimization for Valve-Point Economic Load Dispatch (2010, neutral): “There are a bunch of chaotic sequences, such as logistic map, tent map, Chua’s system, and Lorenz system [25].”
Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems (2019, methodology): “…which we call simulated bifurcation (SB), we numerically simulate adiabatic evolutions of classical nonlinear Hamiltonian systems exhibiting bifurcation phenomena ( 35 ), where two branches of the bifurcation in each non-linear oscillator correspond to two states of each Ising spin ( 30 , 34 ).”
Behavioral dynamics of steering, obstacle avoidance, and route selection. (2003, background): “The form of this shift from one- to two-point attractors is analogous to a tangent bifurcation in a first-order system (Strogatz, 1994).”
Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (2006, background): “subiculum bursting neurons IAHP Stanford et al. (1998) midbrain dopaminergic neurons IK(Ca) Amini et al.”
Control of multistability (2014, background): “This phenomenon known as multistability has be found in almost all natural sciences, including electronics [2], optics [9], mechanics [10], and biology [11].”
Compliant leg behaviour explains basic dynamics of walking and running (2006, background): “1) (Strogatz 2001).”
PREY PREFERENCE BY A TOP PREDATOR AND THE STABILITY OF LINKED FOOD CHAINS (2000, methodology): “The location and extent of the region with a point attractor were related to the correlation dimension of the unlinked three-species food chain (correlation dimension is a measure of the complexity of chaos; Grassberger and Procaccia 1983, Strogatz 1994).”
Complexity and Adaptivity in Supply Networks: Building Supply Network Theory Using a Complex Adaptive Systems Perspective (2007, methodology): “Analysis techniques used within these articles include chaos theory (Strogatz, 1994), computational and statistical mechanics (Shalizi, 2001), and nonlinear time series methods (Williams, 1997).”