A Video Game Based on Elementary Differential Equations


In this paper a prey-predator video game is presented. In the video game two predators chase a prey that tries to avoid the capture by the predators and to reach a location in space (i.e. its “home”). The prey is animated by a human player (using a joypad), the predators are automated players whose behaviour is decided by the video game engine. The purpose of the video game is to show how to use mathematical models to build a simple prey-predator dynamics representing a physical system where the movements of the game actors satisfy Newton’s dynamical principle and the behaviour of the automated players simulates a simple form of intelligence. The game is based on a simple set of ordinary differential equations. These differential equations are used in classical mechanics to describe the dynamics of a set of point masses subject to a force chosen by the human player, elastic forces and friction forces (i.e. viscous damping). The software that implements the video game is written in C++ and Delphi. The video game can be downloaded from:


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M. Giacinti, F. Mariani, M. Recchioni and F. Zirilli, "A Video Game Based on Elementary Differential Equations," Intelligent Control and Automation, Vol. 4 No. 3, 2013, pp. 250-262. doi: 10.4236/ica.2013.43030.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] F. Bellotti, R. Berta and A. De Gloria, “Designing Effec tive Serious Games: Opportunities and Challenges for Research,” Special Issue: Creative Learning with Serious Games, Journal of Emerging Technologies in Learning, Vol. 5, No. 3, 2010, pp. 22-35.
[2] F. Bellotti, R. Berta, A. De Gloria and L. Primavera, “Adaptive Experience Engine for Serious Games,” IEEE Transactions on Computational Intelligence and AI in Games, Vol. 1, No. 4, 2009, pp. 264-280. doi:10.1109/TCIAIG.2009.2035923
[3] M. Athans, “On Optimal Allocation and Guidance Laws for Linear Interception and Rendez Vous Problems,” IEEE Transactions on Aerospace and Electronics Sys tems, Vol. 7, No. 5, 1971, pp. 843-853. doi:10.1109/TAES.1971.310324
[4] R. Isaacs, “Differential Games,” Dover Publication, New York, 1999.
[5] A. A. Melikyan, “Primary Strategies of Simple Pursuit in Differential Games on Two-Sided Plane Figures,” Journal of Applied Mathematics and Mechanics, Vol. 68, No. 4, 2004, pp. 545-554. doi:10.1016/j.jappmathmech.2004.07.007
[6] V. Kokkeviv, “Practical Physics for Articulated Charac ters,” Game Developers Conference, San Jose, 24-26 2004, pp. 1-16. http://www.red3d.com/cwr/games/#ai-papers
[7] I. Millington, “Game Physics Engine Developments,” El sevier Inc., San Francisco, 2007.
[8] S. I. Nishimura and T. Ikegami, “Emergence of Collective Strategies in a Prey-Predator Game Model,” Artificial Life, Vol. 3, No. 4, 1997, pp. 243-260. doi:10.1162/artl.1997.3.4.243
[9] I. Millington, “Artificial Intelligence for Games,” Morgan Kaufmann Publications, Elsevier, San Francisco, 2006.
[10] V. Y. Glizer and V. Turetsky, “Complete Solution of a Differential Game with Linear Dynamics and Bounded Controls,” Applied Mathematics Research Express, Vol. 2008, No. 1, 2008, 49 p. doi:10.1093/amrx/abm012

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