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

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.

Identifying novel molecular mechanisms of ghrelin receptor signalling underlying neural control of food intake: interaction with stress and impulsivity

The gut-hormone, ghrelin, activates the centrally expressed growth hormone secretagogue 1a (GHS-R1a) receptor, or ghrelin receptor. The ghrelin receptor is a G-protein coupled receptor (GPCR) expressed in several brain regions, including the arcuate nucleus (Arc), lateral hypothalamus (LH), ventral tegmental area (VTA), nucleus accumbens (NAcc) and amygdala. Activation of the GHS-R1a mediates a multitude of biological activities, including release of growth hormone and food intake. The ghrelin signalling system also plays a key role in the hedonic aspects of food intake and activates the dopaminergic mesolimbic circuit involved in reward signalling. Recently, ghrelin has been shown to be involved in mediating a stress response and to mediate stress-induced food reward behaviour via its interaction with the HPA-axis at the level of the anterior pituitary. Here, we focus on the role of the GHS-R1a receptor in reward behaviour, including the motivation to eat, its anxiogenic effects, and its role in impulsive behaviour. We investigate the functional selectivity and pharmacology of GHS-R1a receptor ligands as well as crosstalk of the GHS-R1a receptor with the serotonin 2C (5-HT2C) receptor, which represent another major target in the regulation of eating behaviour, stress-sensitivity and impulse control disorders. We demonstrate, to our knowledge for the first time, the direct impact of GHS-R1a signalling on impulsive responding in a 2-choice serial reaction time task (2CSRTT) and show a role for the 5-HT2C receptor in modulating amphetamine-associated impulsive action. Finally, we investigate differential gene expression patterns in the mesocorticolimbic pathway, specifically in the NAcc and PFC, between innate low- and high-impulsive rats. Together, these findings are poised to have important implications in the development of novel treatment strategies to combat eating disorders, including obesity and binge eating disorders as well as impulse control disorders, including, substance abuse and addiction, attention deficit hyperactivity disorder (ADHD) and mood disorders.