Analyzing the Stability of Lanchester Warfare Models for Symmetric Warfare Scenarios

  • Authors

    • Rapheal Oladipo Fifelola Department of Mathematical Sciences, Faculty of Sciences, Nigerian Defence Academy.
    • OKAFOR UCHENWA LINUS DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCES, NIGERIAN DEFENCE ACADEMY.
    • ADEDAPO KEHINDE FEMI DEPARTMENT OF PHYSICAL AND CHEMICAL SCIENCES,FEDERAL UNIVERSITY OF HEALTH SCIENCES
    2024-07-22
    https://doi.org/10.14419/4j2s5d90
  • Lanchester models, symmetric warfare, stability analysis, mathematical modeling, conflict dynamics.

  • This study analyzes the stability of Lancaster-type ODE models in symmetric warfare situations. In symmetric warfare situations, when the lethality coefficients (K) are equal for both forces in battle, the system exhibits marginal stability, characterized by poles at ± K, indicating that the model is stable in some regions and unstable in others. The present research illustrates a controlled rhythmicity, and these forces show a harmonized balance between the two battling forces in order to develop a strong strategy and decision for military.

  • References

    1. T. M. Apostol, Calculus, Volume II. John Wiley & Sons, 1967.
    2. J. Bracken, Lanchester models of the Ardennes campaign, Naval Research Logistics (NRL), 42(4), 559-577, 1995.
    3. N. Cangiotti, M. Capolli, M. Sensi, A generalization of unaimed fire Lanchester’s model in multi-battle warfare, Journal of Operational Research, 23(38), 2023.
    4. X. Chen, Y. Jing, C. Li, M. Li, Warfare command stratagem analysis for winning based on Lanchester attrition models, Journal of Systems Science and Systems Engineering, 21(1), 94-105, 2012.
    5. S. J. Deitchman, A Lanchester Model of Guerrilla Warfare, Journal of Operations Research, 10(6), 818-827, 1962.
    6. A. Hurwitz, Ueber die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt, Mathematische Annalen, 46(2), 273-284, 1895.
    7. X. Ji, W. Zhang, F. Xiang, W. Yuan, J. Chen, A Swarm Confrontation Method Based on Lanchester Law and Nash Equilibrium, Electronics, 11(6), 896, 2022.
    8. A. C. Kalloniatis, K. Hoek, M. Zuparic, M. Brede, Optimising structure in a networked Lanchester model for fires and manoeuvre in warfare, Journal of Systems Science and Applied Mathematics, 29(6), 1863-1878, 2020.
    9. Y. L. Kyle, N. J. MacKay, The optimal policy for the one-against-many heterogeneous Lanchester model, Operations Research Letters, 42(6–7), 473-477, 2014.
    10. M. Kress, Lanchester Models for Irregular Warfare, Mathematics, 8(5), 737, 2020.
    11. M. Kress, J. P. Caulkins, G. Feichtinger, D. Grass, A. Seidl, Lanchester model for three-way combat, European Journal of Operational Research, 264(1), 46-54, 2018.
    12. F. W. Lanchester, Aircraft in warfare: The dawn of the fourth arm (with introductory preface by David Henderson), Kessinger Publishing, 2010.
    13. L. C. Piccinini, G. Stampacchia, G. Vidossich, Ordinary Differential Equations in Rn, Springer-Verlag, 1984.
    14. V. Protopopescu, R. T. Santoro, R. L. Cox, P. Rusu, Combat modeling with partial differential equations: The bidimensional case (Technical Report), 1990.
    15. E. J. Routh, A Treatise on the Stability of a Given State of Motion: Particularly Steady Motion, Macmillan, 1877.
    16. C. Spradlin, G. Spradlin, Extended Lanchester's Equations: Exploring Multi-Dimensional Combat Dynamics, Journal of Mathematical Warfare, 5(1), 1-23, 2007.
    17. J. G. Taylor, Target Selection in Lanchester Combat: Linear-Law Attrition Process, Journal of Operations Research, 21(5), 1136-1143, 1971.
    18. J. G. Taylor, Battle-Outcome Prediction for an Extended System of Lanchester-Type Differential Equations, Journal of Mathematical Analysis and Applications, 103(2), 371-379, 1984.
    19. J. G. Taylor, G. G. Brown, Numerical Determination of the Parity-Condition Parameter for Lanchester-Type Equations of Modern Warfare, Journal of Computer & Operations Research, 5(4), 227-242, 1978.
    20. J. Bracken, Lanchester models of the Ardennes campaign, Naval Research Logistics (NRL), 42(4), 559-577, 1995.

  • Downloads

  • How to Cite

    Fifelola, R. O., OKAFOR UCHENWA LINUS, & ADEDAPO KEHINDE FEMI. (2024). Analyzing the Stability of Lanchester Warfare Models for Symmetric Warfare Scenarios. International Journal of Applied Mathematical Research, 13(2), 69-73. https://doi.org/10.14419/4j2s5d90