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Approximating the Stability Region for a Differential Equation with a Distributed Delay

S. A. CampbellR. Jessop — 2009

Mathematical Modelling of Natural Phenomena

We discuss how distributed delays arise in biological models and review the literature on such models. We indicate why it is important to keep the distributions in a model as general as possible. We then demonstrate, through the analysis of a particular example, what kind of information can be gained with only minimal information about the exact distribution of delays. In particular we show that a stability region may be obtained in a similar way that delay independent results are obtained for systems...

Indecision in Neural Decision Making Models

J. MiltonP. NaikC. ChanS. A. Campbell — 2010

Mathematical Modelling of Natural Phenomena

Computational models for human decision making are typically based on the properties of bistable dynamical systems where each attractor represents a different decision. A limitation of these models is that they do not readily account for the fragilities of human decision making, such as “choking under pressure”, indecisiveness and the role of past experiences on current decision making. Here we examine the dynamics of a model of two interacting neural populations with mutual time–delayed inhibition....

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