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

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dc.contributor.advisor Rachinskii, Dmitrii en
dc.contributor.author McCarthy, Stephen P.
dc.date.accessioned 2013-05-27T12:19:42Z
dc.date.available 2013-05-27T12:19:42Z
dc.date.issued 2013
dc.date.submitted 2013
dc.identifier.citation McCarthy, S.P. 2013. Differential and numerical models of hysteretic systems with stochastic and deterministic inputs. PhD Thesis, University College Cork. en
dc.identifier.endpage 111
dc.identifier.uri http://hdl.handle.net/10468/1138
dc.description.abstract Many 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.format.mimetype application/pdf en
dc.language.iso en en
dc.publisher University College Cork en
dc.rights © 2013. Stephen McCarthy en
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/ en
dc.subject Bacteria growth model with hysteresis en
dc.subject Price dynamics model with memory en
dc.subject Stochastic differential equation with hysteresis en
dc.subject.lcsh Hysteresis en
dc.subject.lcsh Stochastic differential equations en
dc.subject.lcsh Bacterial growth--Mathematical models en
dc.subject.lcsh Prices--Mathematical models en
dc.title Differential and numerical models of hysteretic systems with stochastic and deterministic inputs en
dc.type Doctoral thesis en
dc.type.qualificationlevel Doctoral en
dc.type.qualificationname PhD (Science) en
dc.internal.availability Full text available en
dc.check.info No embargo required en
dc.description.version Accepted Version
dc.description.status Not peer reviewed en
dc.internal.school Mathematics en
dc.check.type No Embargo Required
dc.check.reason No embargo required en
dc.check.opt-out Not applicable en
dc.thesis.opt-out false *
dc.check.embargoformat Not applicable en
ucc.workflow.supervisor d.rachinskii@ucc.ie *


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