Journal ArticleDOI
Qualitative Analysis of Critical Transitions in Complex Disease Propagation from a Dynamical Systems Perspective
Gang Wang,Xiufen Zou +1 more
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TLDR
Three indicators are theoretically derived that serve as a general early-warning signal indicating an imminent bifurcation or sudden deterioration before the critical transition occurs of dynamical systems from a new perspective.Abstract:
Considerable evidence suggests that in complex diseases the deteriorations are often abrupt, and can be viewed as a bifurcation or a critical transition from one asymptotically stable equilibrium to another one at a tipping point. Here, we propose some new ideas to detect early-warning signals of such critical transitions from the perspective of qualitative theory of ordinary differential equations. Specifically, we theoretically derive three indicators that serve as a general early-warning signal indicating an imminent bifurcation or sudden deterioration before the critical transition occurs. Then, we verify our theoretical results by numerical simulations for three examples. Our work forms a starting point to motivate new mathematical insights into predictability for critical transitions of dynamical systems from a new perspective.read more
Citations
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Predicting rock failure with the critical slowing down theory
TL;DR: In this paper, the authors examined the critical slowing down characteristics of acoustic emission (AE) and precursory signals preceding catastrophic rock failure, and verified the applicability and reliability of precursary signals through the Critical slowing down theory by statistically analysing the laboratory data from a wide range of rocks.
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The precursory information of acoustic emission during sandstone loading based on critical slowing down theory
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KCC Analysis of a One-Dimensional System During Catastrophic Shift of the Hill Function: Douglas Tensor in the Nonequilibrium Region
TL;DR: The stability of a one-dimensional system during a catastrophic shift described by the Hill function is considered, because the shifting process goes through a nonequilibrium region.
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Epileptic seizure prediction in intracranial EEG using critical nucleus based on phase transition.
TL;DR: In this paper , the authors used three key measures of fluctuation, correlation and percolation to quantify preictal states of epilepsy and proposed a critical nucleus model combined with spatial and temporal features of iEEG signals capable of seizure prediction.
References
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TL;DR: Recent studies show that a loss of resilience usually paves the way for a switch to an alternative state, which suggests that strategies for sustainable management of such ecosystems should focus on maintaining resilience.
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Elements of applied bifurcation theory
TL;DR: One-Parameter Bifurcations of Equilibria in continuous-time systems and fixed points in Discrete-Time Dynamical Systems have been studied in this paper, where they have been used for topological equivalence and structural stability of dynamical systems.
Journal ArticleDOI
Early-warning signals for critical transitions
Marten Scheffer,Jordi Bascompte,William A. Brock,Victor Brovkin,Stephen R. Carpenter,Vasilis Dakos,Hermann Held,Egbert H. van Nes,Max Rietkerk,George Sugihara +9 more
TL;DR: Work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.
Journal ArticleDOI
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering
TL;DR: This book discusses Chaos, Fractals, and Dynamics, and the Importance of Being Nonlinear in a Dynamical View of the World, which aims to clarify the role of Chaos in the world the authors live in.