Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Volume 21, Issue 1, Pages 227-243Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdsb.2016.21.227
Keywords
Multi-stability; hysteresis; gradient system; heteroclinic connection; graph
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Funding
- NSF [DMS-1413223]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1413223] Funding Source: National Science Foundation
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We consider gradient systems with an increasing potential that depends on a scalar parameter. As the parameter is varied, critical points of the potential can be eliminated or created through saddle-node bifurcations causing the system to transit from one stable equilibrium located at a (local) minimum point of the potential to another minimum along the heteroclinic connections. These transitions can be represented by a graph. We show that any admissible graph has a realization in the class of two dimensional gradient flows. The relevance of this result is discussed in the context of genesis of hysteresis phenomena. The Preisach hysteresis model is considered as an example.
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