Research Article
Bifurcation Analysis and Multiobjective Nonlinear Model Predictive Control of Sustainable Ecosystems
Issue:
Volume 9, Issue 3, September 2024
Pages:
37-43
Received:
1 October 2024
Accepted:
17 October 2024
Published:
11 November 2024
DOI:
10.11648/j.ijssam.20240903.11
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Abstract: Objective: All optimal control work involving ecological models involves single objective optimization. In this work, we perform multiobjective nonlinear model predictive control (MNLMPC) in conjunction with bifurcation analysis on an ecosystem model. Methods: Bifurcation analysis was performed using the MATLAB software MATCONT while the multi-objective nonlinear model predictive control was performed by using the optimization language PYOMO. Results: Rigorous proof showing the existence of bifurcation (branch) points is presented along with computational validation. It is also demonstrated (both numerically and analytically) that the presence of the branch points was instrumental in obtaining the Utopia solution when the multiobjective nonlinear model prediction calculations were performed. Conclusions: The main conclusions of this work are that one can attain the utopia point in MNLMPC calculations because of the branch points that occur in the ecosystem model and the presence of the branch point can be proved analytically. The use of rigorous mathematics to enhance sustainability will be a significant step in encouraging sustainable development. The main practical implication of this work is that the strategies developed here can be used by all researchers involved in maximizing sustainability The future work will involve using these mathematical strategies to other ecosystem models and food chain models which will be a huge step in developing strategies to address problems involving nutrition.
Abstract: Objective: All optimal control work involving ecological models involves single objective optimization. In this work, we perform multiobjective nonlinear model predictive control (MNLMPC) in conjunction with bifurcation analysis on an ecosystem model. Methods: Bifurcation analysis was performed using the MATLAB software MATCONT while the multi-obje...
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Research Article
Stability Analysis of Asymmetric Warfare Dynamics Using the Lanchester Ordinary Differential Equation Model Through Jacobian Linearization and Energy Analysis
Rapheal Oladipo Fifelola*
,
Sydney Chinedu Osuala,
Adedapo Kehinde Femi
Issue:
Volume 9, Issue 3, September 2024
Pages:
44-54
Received:
13 December 2024
Accepted:
2 January 2025
Published:
7 January 2025
DOI:
10.11648/j.ijssam.20240903.12
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Views:
Abstract: This paper investigates the stability of the Lanchester Ordinary Differential Equation (ODE) in asymmetric warfare, where two forces with differing lethality coefficients engage. The system exhibits marginal stability at the equilibrium point after linearization, characterized by purely imaginary eigenvalues, indicating that the forces are balanced but without a definitive resolution. An energy-based analysis further supports this by identifying a characteristic frequency associated with the interaction of the forces. These findings suggest that asymmetric warfare scenarios are inherently prone to sustained oscillations, reflecting a dynamic equilibrium between the opposing forces. The presence of these oscillations indicates that while the forces may not decisively defeat one another, a long-term balance persists, preventing either side from achieving a clear victory. The results imply that asymmetric warfare is likely to lead to prolonged conflicts with no easy resolution, as the dynamics between the forces result in cyclical patterns of attack and defense. This work highlights the importance of understanding the stability of such systems, providing insights into the potential for sustained conflict when forces are unequal. The study contributes to the broader understanding of conflict dynamics, offering valuable perspectives on how these imbalances affect the course of warfare. The findings could inform military strategy, particularly in planning for engagements where one side holds a clear advantage over the other but still faces persistent resistance.
Abstract: This paper investigates the stability of the Lanchester Ordinary Differential Equation (ODE) in asymmetric warfare, where two forces with differing lethality coefficients engage. The system exhibits marginal stability at the equilibrium point after linearization, characterized by purely imaginary eigenvalues, indicating that the forces are balanced...
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