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Qualitative Analysis of Critical Transitions in Complex Disease Propagation from a Dynamical Systems Perspective.
- Source :
-
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering . Dec2016, Vol. 26 Issue 14, p-1. 18p. - Publication Year :
- 2016
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02181274
- Volume :
- 26
- Issue :
- 14
- Database :
- Academic Search Index
- Journal :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 120746095
- Full Text :
- https://doi.org/10.1142/S0218127416502394