A theoretical predator prey / obligate mutualism model of information security is extended to allow for some of the parameters to be non-constant and dependent on security. A numerical example demonstrates the evolution of the critical point as security increases. The system encounters two phase changes: from three dimensions to two dimensions as attackers disappear and then to a null solution as users disappear. In the two dimensional sub-problem, the critical point farther from the origin is stable. The impact of security changes in the 3D case is illustrated with graphical estimation of the basins of attraction of the critical points.

Addicott, J. (1981). Stability Properties of a 2-Species Models Of Mutualism: Simulation Studies. Oceologiia 49 (42-49, 42-49.

Addicott, J. and Freedman, H. (1984). On The Structure And Stability Of Mutualistic Systems: Analysis Of Predator –Prey And Competition Models As Modified By The Action of a Slow Growing Mutualist. Theoretical Population Biology, 26, 320-229.

Becker, G. S. (1968). Crime and punishment: An economic approach. J. of Political Economy, 78, 169-217.

Boyce, W. and Diprima, P. (2005). Elementary Differential Equations (8th ed.). Hobokan: Wiley.

Brauer, F. and Chavez, C. C. (2000). Mathematical Models In Population Biology and Epidemiology. New York: Springer-Verlag.

Bronstein, J. (1994). Our Current Understanding of Mutualism. Quarterly Review of Biology, 69, (31-51.

Cavoretto, R., Chaudhuri, S., DeRossi, A., Menduni, E., Moretti, F., Rodi, M. C., and Venturino, E. (2011). Approximation of Dynamical System's Separatrix Curves. AIP Conference Proc. https://doi.org/10.1063/1.3637836. Retrieved from AIP eb site.

D'Arcy, J., Herath, T., and Shoos, M. (2014). Understanding Employee Responses to Stressful Information Security Requirements: A Coping Perspective. Journal of Management Information Systems, 32(2).

Dutta, A. and Roy, R. (2008). Dynamics of Organizational Information Security. Systems Dynamics Review 24#3, 349-375.

Freedman, H., Addicott, J., and Rai, B. (1987). Obligate Mutualism With A Predator: Stability And Persistence Of Three Species Models. 32. Theoretical Population Biology, 32, 157-175.

Pendegraft, N. (2017). Predator-prey / Obligate Mutualism in Information System Security and Usage. Journal of Information Technology Theory and Application, 18(1), 5-45.

Pendegraft, N. and Rounds, M. (2007). A Simulation Model of IS Security. International Journal of Information Security and Privacy, 1.

Rai, B. F. (1983). Analysis of Three Species Models of Mutualism In Predator-Prey And Competitive Systems. Mathematical Biosciences, 65, 13-50.

Rounds, M., Alves-Foss, J., and Pendegraft, N. (2013). An Experimental Study to Explore Response to Changes in Security and Reward. 46th Annual Hawaii International Conference on System Sciences,. 2969-2977.

Rounds, M., Pendegraft, N., and Taylor, C. (2007). The Ecology of IS Security: A Research Agenda. Information Resources Management Association International Meeting. Vancouver, B.C.

Saltzer, J. and Schrodeder, M. (1975). The Protection of information in computer systems. Proceedings of the IEEE 63#9, 1278-1308.

Senge, P. (1990). The Fifth Discipline. New York.: Currency Doubleday.

Sterman, J. (2000). Business Dynamics. Boston. : McGraw Hill.

Tarafdar, M., D'Arcy, J., Turel, O. and Ashish, G. (2015, Winter). The Dark Side of Information Technology. MIT Sloan Management Review, 61-70.

Zedner, L. (2003). Too Much Security. International Journal of the Sociology of Law, 31(3), 155-184.