A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most predictive models are shown to be based on variations of the classical Verhulst logistic growth equation. We review and compare several such models and analyse properties of interest for these. We also identify and detail several associated limitations and restrictions.A generalized form of the logistic growth curve is introduced which incorporates these models as special cases. Several properties of the generalized growth are also presented. We furthermore prove that the new growth form incorporates additional growth models which are markedly different from the logistic growth and its variants, at least in their mathematical representation. Finally, we give a brief outline of how the new curve could be used for curve-fitting.

It has been suggested by many supply chain practitioners that in certain cases inventory can have a stimulating effect on the demand. In mathematical terms this amounts to the demand being a function of the inventory level alone. In this work we propose a logistic growth model for the inventory dependent demand rate and solve first the continuous time deterministic optimal control problem of maximising the present value of the total net profit over an infinite horizon. It is shown that under a strict condition there is a unique optimal stock level which the inventory planner should maintain in order to satisfy demand. The stochastic version of the optimal control problem is considered next. A bang-bang type of optimal control problem is formulated and the associated Hamilton-Jacobi-Bellman equation is solved. The inventory level that signifies a switch in the ordering strategy is worked out in the stochastic case.

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In this paper I propose a reinforcement learning model for a predator preying upon two types of prey, the unpalatable (noxious) models, and the palatable mimics. The latter type of prey resembles the models in appearance so as to derive some protection from the predator who must avoid the unpalatable models. Essentially the predator is treated as a learning automaton adopting a simple reinforcement learning strategy in order to increase its consumption of palatable prey and reduce the consumption of unpalatable ones. The populations of both mimics and models are assumed to grow logistically.

In this paper, we utilize a reinforcement learning model for a specialist predator preying upon two types of prey, the noxious models, which are abundant, and the palatable mimics, which are much rarer, in accord with the concept of Batesian mimicry. The latter type of prey resembles the models in appearance so as to derive some protection from the predator who must avoid the unpalatable models. We treat the predator as a slow learning automaton adopting a simple reinforcement learning strategy in order to increase its consumption of palatable prey and reduce the consumption of unpalatable ones. We assume a logistic growth for both models and mimics.