Abstract
The Lotka-Volterra predator-prey model for population dynamics between prey and predator species, has been an important model in Biology for many years. Most recently, it has been used to explain the relationship between Venture Capital investment opportunities and the experience of the investors, which represent the prey and predator respectively. Our work extends this model to include a modification with two investment opportunities available to the venture capitalist. The dynamics of the system are investigated via analytical work and numerical simulations to obtain bifurcation points which affect the stability of the system. Results are presented numerically and graphically. In our study, parameters related to returns to investment experience, investment handling time, rate of conversion of investment opportunities and depreciation of investment experience have threshold values where the system switches from stable to unstable. The stability regions for each of these parameters display suitable ranges. This provides investors with guidance to invest only when these parameters are within the stability regions.
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The authors thank the AMMCS International Conference 2017 for the opportunity to present this work and to Springer for its publication.
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Addison, L.M., Bhatt, B., Owen, D. (2018). Dynamical Analysis of a Modified Prey-Predator Model for Venture Capital Investment. In: Kilgour, D., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Advances in Mathematical and Statistical Methods . AMMCS 2017. Springer Proceedings in Mathematics & Statistics, vol 259. Springer, Cham. https://doi.org/10.1007/978-3-319-99719-3_42
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