Unifying warfighting functions in mathematical modelling: combat, manoeuvre, and C2

References

• Acebrón, J., Bonilla, L., Pérez-Vicente, C., Ritort, F., & Spigler, R. (2005). The Kuramoto model: A simple paradigm for synchronization phenomena. Reviews of Modern Physics, 77(1), 137–183. https://doi.org/10.1103/RevModPhys.77.137
   Web of Science ®Google Scholar
• Adams, E., & Mesterton-Gibbons, M. (2003). Lanchester’s attrition models and fights among social animals. Behavioral Ecology, 14(5), 719–723. https://doi.org/10.1093/beheco/arg061
   Web of Science ®Google Scholar
• Alberts, D., Garstka, J., & Stein, F. (1999). Network centric warfare. Command and Control Research Program.
   Google Scholar
• Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., & Zhou, C. (2008). Synchronization in complex networks. Physics Reports, 469(3), 93–153. https://doi.org/10.1016/j.physrep.2008.09.002
   Web of Science ®Google Scholar
• Boccaletti, S., Bianconi, G., Criado, R., Del Genio, C. I., Gómez-Gardeñes, J., Romance, M., Sendiña-Nadal, I., Wang, Z., & Zanin, M. (2014). The structure and dynamics of multilayer networks. Physics Reports, 544(1), 1–122. https://doi.org/10.1016/j.physrep.2014.07.001
   PubMed Web of Science ®Google Scholar
• Bollobás, B. (2013). Modern graph theory. Springer Science and Business Media.
   Google Scholar
• Bracken, J. (1995). Lanchester models of the Ardennes campaign. Naval Research Logistics, 42(4), 559–577. https://doi.org/10.1002/1520-6750(199506)42:4<559::AID-NAV3220420405>3.0.CO;2-R
   Web of Science ®Google Scholar
• Deitchman, S. (1962). A Lanchester Model of Guerrilla Warfare. Operations Research, 10(6), 818–827. https://doi.org/10.1287/opre.10.6.818
   Web of Science ®Google Scholar
• Demazy, A., Kalloniatis, A., Alpcan, T. (2018). A game theoretic analysis of the Boyd-Kuramoto model [Paper presentation]. Proceedings of 9th International Conference on GameSec 2018: International Conference on Decision and Game Theory for Security, Seattle, WA, USA, October 29–31, pp. 248––264.
   Google Scholar
• Dörfler, F., & Bullo, F. (2014). Synchronization in complex networks of phase oscillators: A survey. Automatica, 50(6), 1539–1564. https://doi.org/10.1016/j.automatica.2014.04.012
   Web of Science ®Google Scholar
• Fricker, R. (1998). Attrition models of the Ardennes campaign. Naval Research Logistics, 45(1), 1–22. https://doi.org/10.1002/(SICI)1520-6750(199802)45:1<1::AID-NAV1>3.0.CO;2-D
   Web of Science ®Google Scholar
• Holder, A., Zuparic, M., & Kalloniatis, A. (2017). Gaussian noise and the two-network frustrated Kuramoto model. Physica D: Nonlinear Phenomena., 341, 10–32. https://doi.org/10.1016/j.physd.2016.09.009
   Web of Science ®Google Scholar
• Hollenbeck, J., & Spitzmueller, M. (2012). Team-structure: Tight versus Loose coupling in task-oriented groups. In S. Kozlowski (Ed.), The Oxford Handbook of Organizational Psychology (Vol. 2, pp. 733–766). Oxford University Press.
   Google Scholar
• Hughes, W. (1995). A salvo model of warships in missile combat used to evaluate their staying power. Naval Research Logistics, 42(2), 267–289. https://doi.org/10.1002/1520-6750(199503)42:2<267::AID-NAV3220420209>3.0.CO;2-Y
   Web of Science ®Google Scholar
• Kalloniatis, A., Hoek, K., Zuparic, M., & Brede, M. (2021). Optimising structure in a networked Lanchester model for fires and manoeuvre in warfare. Journal of the Operational Research Society, 72(8), 1863–1878. https://doi.org/10.1080/01605682.2020.1745701
   Web of Science ®Google Scholar
• Kalloniatis, A., McLennan-Smith, T., & Roberts, D. (2020). Modelling distributed decision making in Command and Control using stochastic network synchronisation. European Journal of Operational Research, 284(2), 588–603. https://doi.org/10.1016/j.ejor.2019.12.033
   Web of Science ®Google Scholar
• Kalloniatis, A., & Zuparic, M. (2016). Fixed points and stability in the two-network frustrated Kuramoto model. Physica A: Statistical Mechanics and Its Applications, 447, 21–35. https://doi.org/10.1016/j.physa.2015.11.021
   Web of Science ®Google Scholar
• Kress, M., Lin, K., & MacKay, N. J. (2018). The attrition dynamics of multilateral war. Operations Research, 66(4), 950–956. https://doi.org/10.1287/opre.2018.1718
   Web of Science ®Google Scholar
• Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. Springer.
   Google Scholar
• Lanchester, F. (1916). Aircraft in warfare: The dawn of the fourth arm. Constable Limited.
   Google Scholar
• Liu, J., Zhao, D., & Wang, F. (2013) Network attacks-defense model based on the improved Lanchester equation [Paper presentation]. Proceedings of the 2013 International Conference on Machine Learning and Cybernetics, Tianjin, China, July 14–17.
   Google Scholar
• Lucas, T., & Turkes, T. (2004). Fitting Lanchester equations to the battles of Kursk and Ardennes. Naval Research Logistics (NRL), 51(1), 95–116. https://doi.org/10.1002/nav.10101
   Web of Science ®Google Scholar
• MacKay, N. (2009). Lanchester models for mixed forces with semi-dynamical target allocation. Journal of the Operational Research Society, 60(10), 1421–1427. https://doi.org/10.1057/jors.2008.97
   Web of Science ®Google Scholar
• McLemore, C., Gaver, D., & Jacobs, P. (2016). A model for geographically distributed combat interactions of swarming naval and air forces. Naval Research Logistics (NRL), 63(7), 562–576. https://doi.org/10.1002/nav.21720
   Web of Science ®Google Scholar
• Morse, P., Kimball, G., & Gass, S. (2003). Methods in operations research. Courier Corporation.
   Google Scholar
• Neisser, U. (1976). Cognition and reality: Principles and implications of cognitive psychology. W.H. Freeman.
   Google Scholar
• O’Keefe, K., & Bettstetter, C. (2019). A review of swarmalators and their potential in bio-inspired computing. Proc. SPIE 10982, Micro- and Nanotechnology Sensors, Systems, and Applications XI, 109822E (13 May 2019). doi: 10.1117/12.2518682.
   Google Scholar
• Osinga, F. (2006). Science, strategy and war: The strategic theory of John Boyd (strategy and history). Routledge.
   Google Scholar
• Pecora, L., & Carroll, T. (1998). Master stability functions for synchronized coupled systems. Physical Review Letters, 80(10), 2109–2112. https://doi.org/10.1103/PhysRevLett.80.2109
   Web of Science ®Google Scholar
• Perrow, C. (2011). Normal accidents: Living with high risk technologies (Updated edition). Princeton University Press.
   Google Scholar
• Plowes, N., & Adams, E. (2005). An empirical test of Lanchester’s square law: Mortality during battles of the fire ant Solenopsis invicta. Proceedings of the Royal Society B: Biological Sciences, 272(1574), 1809–1814. https://doi.org/10.1098/rspb.2005.3162
   PubMed Web of Science ®Google Scholar
• Polybius. (1927). The histories. Harvard University Press.
   Google Scholar
• Reid, P. (2007). A brief history of medieval warfare: The rise and fall of English supremacy at arms, 1314–1485. Running Press.
   Google Scholar
• Roberson, B. (2006). The colonel blotto game. Economic Theory, 29(1), 1–24. https://doi.org/10.1007/s00199-005-0071-5
   Web of Science ®Google Scholar
• Rodrigues, F., Peron, T., Ji, P., & Kurths, J. (2016). The Kuramoto model in complex networks. Physics Reports, 610, 1–98. https://doi.org/10.1016/j.physrep.2015.10.008
   Web of Science ®Google Scholar
• Sakaguchi, H., & Kuramoto, Y. (1986). A soluble active rotator model showing phase transitions via mutual entrainment. Progress of Theoretical Physics, 76(3), 576–581. https://doi.org/10.1143/PTP.76.576
   Google Scholar
• Schaffer, M. (1968). Lanchester models of Guerrilla engagements. Operations Research, 16(3), 457–488. https://doi.org/10.1287/opre.16.3.457
   Web of Science ®Google Scholar
• Stanescu, M., Barriga, N., & Buro, M. (2015). Using Lanchester attrition laws for combat prediction in StarCraft [Paper presentation]. Proceedings of the Eleventh AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment (AIIDE-15), Santa Cruz, CA, USA, November 14–18.
   Google Scholar
• Van Creveld, M. (1985). Command in war. Harvard University Press.
   Google Scholar
• Weick, K. (1976). Educational organizations as loosely coupled systems. Administrative Science Quarterly, 21(1), 1–19. https://doi.org/10.2307/2391875
   Web of Science ®Google Scholar
• Zuparic, M., Angelova, M., Zhu, Y., & Kalloniatis, A. (2021). Adversarial decision strategies in multiple network phased oscillators: The Blue-Green-Red Kuramoto-Sakaguchi model. Communications in Nonlinear Science and Numerical Simulation, 95, 105642. https://doi.org/10.1016/j.cnsns.2020.105642
   Web of Science ®Google Scholar