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oai:cora.ucc.ie:10468/11382023-04-04T07:09:08Zcom_10468_388com_10468_5com_10468_1com_10468_88col_10468_389col_10468_140col_10468_859

Not applicable No embargo required Not applicable No embargo required No Embargo Required Rachinskii, Dmitrii McCarthy, Stephen P. 2013-05-27T12:19:42Z 2013-05-27T12:19:42Z 2013 2013 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. Not peer reviewed Accepted Version application/pdf McCarthy, S.P. 2013. Differential and numerical models of hysteretic systems with stochastic and deterministic inputs. PhD Thesis, University College Cork. 111 https://hdl.handle.net/10468/1138 en University College Cork © 2013. Stephen McCarthy http://creativecommons.org/licenses/by-nc-nd/3.0/ Bacteria growth model with hysteresis Price dynamics model with memory Stochastic differential equation with hysteresis Hysteresis Stochastic differential equations Bacterial growth--Mathematical models Prices--Mathematical models false Differential and numerical models of hysteretic systems with stochastic and deterministic inputs Doctoral thesis Doctoral PhD (Science) d.rachinskii@ucc.ieinfo:eu-repo/semantics/openAccess