Qualitative analysis of a tourism area life cycle model for interacting tourism destinations by M. Rodrigo, I. Ajala, A.K. Irhanida

“…Three types of interaction dynamics are investigated: competition, mutualism (or cooperation) and predator–prey. Using dynamical systems theory, aqualitative analysis of the proposed model is performed and all possible tourist equilibria are identified. …”
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Tutorial on Feedback Control of Flows, Part II: Diagnostics and Feedback Control of Mixing by Ole M. Aamo, Thor I. Fossen

“…Diagnostic tools from dynamical systems theory are presented that enable detection and quantification of chaotic transport in periodically perturbed systems. …”
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Temporal Asymmetry, Entropic Irreversibility, and Finite-Time Thermodynamics: From Parmenides–Einstein Time-Reversal Symmetry to the Heraclitan Entropic Arrow of Time by Wassim M. Haddad

“…In this paper, we combine the two universalisms of thermodynamics and dynamical systems theory to develop a dynamical system formalism for classical thermodynamics. …”
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Corticosterone oscillations during mania induction in the lateral hypothalamic kindled rat-Experimental observations and mathematical modeling. by Osama A Abulseoud, Man Choi Ho, Doo-Sup Choi, Ana Stanojević, Željko Čupić, Ljiljana Kolar-Anić, Vladana Vukojević

“…Synergistic combination of the LHK rat model and dynamical systems theory allows us to quantitatively characterize changes in HPA axis activity under controlled induction of acute manic-like states and provides a framework to study in silico how the dynamic integration of neurochemical transformations underlying the HPA axis is disrupted in these states.…”
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Sensitive dependence of trajectories on tracer seeding positions – coherent structures in German Bight backward drift simulations by U. Callies

“…Lines across which drift behaviour changes non-smoothly are obtained as ridges in the fields of the finite-time Lyapunov exponent (FTLE), a parameter used in dynamical systems theory to identify Lagrangian coherent structures (LCSs). …”
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Vector Field Driven Design for Lightweight Signal Processing and Control Schemes for Autonomous Robotic Navigation by Nebu John Mathai, Takis Zourntos, Deepa Kundur

“…We use control and dynamical systems theory both as a description language and as a synthesis toolset to rigorously develop our computational machinery; these mechanisms are mated with structural insights from behavior-based robotics to compose overall algorithmic architectures. …”
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OSCILLATORY AND COMPETING INSTABILITIES IN A NONLINEAR MODEL FOR LANGMUIR CIRCULATIONS by Moroz, I, Leibovich, S

“…Techniques from dynamical systems theory are used to derive equations which describe nonlinear oscillatory convection and the multiple bifurcation, whose character has been explored in the literature. …”

Not All Roads Lead to Resilience: a Complex Systems Approach to the Comparative Analysis of Tortoises in Arid Ecosystems by Thomas E. J. Leuteritz, Hamid R. Ekbia

“…We borrow the notions of control parameter and collective variable from dynamical systems theory to hypothesize that in present-day societies, social parameters might in fact be the control parameters of the greater social-ecological system, and that resilience is the collective variable that captures and demonstrates the overall behavior of the system.…”
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Estimating the stochastic bifurcation structure of cellular networks. by Carl Song, Hilary Phenix, Vida Abedi, Matthew Scott, Brian P Ingalls, Mads Kaern, Theodore J Perkins

“…High throughput measurement of gene expression at single-cell resolution, combined with systematic perturbation of environmental or cellular variables, provides information that can be used to generate novel insight into the properties of gene regulatory networks by linking cellular responses to external parameters. In dynamical systems theory, this information is the subject of bifurcation analysis, which establishes how system-level behaviour changes as a function of parameter values within a given deterministic mathematical model. …”
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Coupled quintessence and the impossibility of an interaction: a dynamical analysis study by Fabrízio F. Bernardi, Ricardo G. Landim

“…Abstract We analyze the coupled quintessence in the light of the linear dynamical systems theory, with two different interactions: (1) proportional to the energy density of the dark energy and (2) proportional to the sum of the energy densities of the dark matter and dark energy. …”
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Multi-condensate state as a functional strategy to optimize the cell signaling output by Aniruddha Chattaraj, Eugene I. Shakhnovich

“…We combine Langevin dynamics, reaction-diffusion simulation, and dynamical systems theory to demonstrate that MCS can indeed be a function optimization strategy. …”
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The Law of Scale Independence by Jonathan D. Phillips

“…The LSI is evaluated here from five independent perspectives: geographic intuition, dynamical systems theory, Kolmogorov entropy, hierarchy theory, and algebraic graph theory. …”
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Study of self-oscillations of a distributed rotor from a material with hereditarily elastic properties by E.P. Kubyshkin

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Catastrophic Regime Shift in Water Reservoirs and São Paulo Water Supply Crisis. by Renato M Coutinho, Roberto A Kraenkel, Paulo I Prado

“…These results highlight the broader aspect that reservoir management must account for their intrinsic bistability, and should benefit from dynamical systems theory. Our case study illustrates the catastrophic consequences of failing to do so.…”
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Coevolving institutions and the paradox of informal constraints by Seligson, Daniel, McCants, Anne EC

“…In this paper, we propose a new theory that is: grounded in institutions as coevolving sources of economic growth rather than as rules constraining growth; and deployed in dynamical systems theory rather than game theory. We show that with our approach some long-standing problems are resolved, in particular, the paradoxical and perplexingly pervasive influence of informal constraints on the long-run character of economies.…”
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Singular vectors, predictability and ensemble forecasting for weather and climate by Palmer, T, Zanna, L

“…This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Lyapunov analysis: from dynamical systems theory to applications'. © 2013 IOP Publishing Ltd.…”

A patchy model for tick population dynamics with patch-specific developmental delays by Marco Tosato, Xue Zhang, Jianhong Wu

“…We obtain a coupled system of four delay differential equations with two delays, and we examine how the dynamical behaviours depend on patch-specific basic reproduction numbers and host mobility by using singular perturbation analyses and monotone dynamical systems theory. Our theoretical results and numerical simulations provide useful insights for tick population control strategies.…”
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Automated Techniques for the Qualitative Analysis of Ecological Models: Continuous Models by Lynn van Coller

“…In this paper, I demonstrate how various computer packages can aid qualitative analyses by implementing techniques from dynamical systems theory. Because computer software is used to obtain the results, the techniques can be used by nonmathematicians as well as mathematicians. …”
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Survival and weak chaos by Sean Nee

“…Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. …”
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Identifying a developmental transition in honey bees using gene expression data. by Bryan C Daniels, Ying Wang, Robert E Page, Gro V Amdam

“…These transitions can be related to bifurcations (or critical points) in dynamical systems theory. Characterizing these collective transitions is a major challenge for systems biology. …”
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