Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

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dc.check.embargoformatNot applicableen
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dc.contributor.advisorRachinskii, Dmitriien
dc.contributor.authorMcCarthy, Stephen P.
dc.date.accessioned2013-05-27T12:19:42Z
dc.date.available2013-05-27T12:19:42Z
dc.date.issued2013
dc.date.submitted2013
dc.description.abstractMany deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.en
dc.description.statusNot peer revieweden
dc.description.versionAccepted Version
dc.format.mimetypeapplication/pdfen
dc.identifier.citationMcCarthy, S.P. 2013. Differential and numerical models of hysteretic systems with stochastic and deterministic inputs. PhD Thesis, University College Cork.en
dc.identifier.endpage111
dc.identifier.urihttps://hdl.handle.net/10468/1138
dc.language.isoenen
dc.publisherUniversity College Corken
dc.rights© 2013. Stephen McCarthyen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/en
dc.subjectBacteria growth model with hysteresisen
dc.subjectPrice dynamics model with memoryen
dc.subjectStochastic differential equation with hysteresisen
dc.subject.lcshHysteresisen
dc.subject.lcshStochastic differential equationsen
dc.subject.lcshBacterial growth--Mathematical modelsen
dc.subject.lcshPrices--Mathematical modelsen
dc.thesis.opt-outfalse*
dc.titleDifferential and numerical models of hysteretic systems with stochastic and deterministic inputsen
dc.typeDoctoral thesisen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhD (Science)en
ucc.workflow.supervisord.rachinskii@ucc.ie*
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