3D Chaotic Nonlinear Dynamic Population-Growing Mathematical System Modeling with Multiple Controllers

Abstract

Modeling, stabilization, and identification processes are significant stages in the process of developing knowledge about chaotic dynamical systems which entail the effective prediction depending on the degree of uncertainty toleration in the forecast, accuracy of the current state to be measured as well as a time scale resting on the dynamics of the system. Control of under-activated dynamical systems has been considered substantially, and it is for periods and is currently developing in various domains such as biology, data analysis, computing systems, and so forth. Dynamic systems of growing population signifies a model describing the way a population evolves over time during which population goes through major life events, split into discrete time periods. The size of the population at a given time period is determined by the rate of growth as well as other related factors. Most progress has been made in model-based control theory, which has drawbacks when the system under consideration is exceedingly complicated, and no model can be constructed. Accordingly, a 3D-discrete and dynamic human population growth system with many controllers is proposed by examining the stability and symmetry of controller system clarifications. The symmetric stability control results are presented by considering a special parametric dynamic system in its coefficients besides suggesting periodic functional coefficients in terms of sin and cos functions. The controllers have the ability to reduce population growth rate unpredictability or enhance system stability under various external conditions. The unique and very effective strategies in relevant domains could provide a deeper understanding of their impact as well as the theoretical or technological innovations thereof. These controllers are capable of reducing population growth rate unpredictability or improving system stability under various external conditions, and applicable strategies in the relevant domains can provide profound comprehension over the impact along with the theoretical as well as technological advancements.

Keywords

• Control system
• Dynamic system
• Difference system
• Stability analysis
• Growing human population
• Stabilization
• Mathematical modeling
• 3D-discrete chaotic systems
• Kendall coefficient
• Discrete systems
• Difference equation
• Multiple controllers
• Jacobian matrix model

References

1. Dhinakaran V., N. M. A.-S. K. R. S. J., Hayder N. and I. H., 2021 A new megastable chaotic oscillator with blinking oscillation terms. Complexity 2021: 1–12.
2. H. Natiq, S. J. O. M. N. M. . A. K. F., N. M. Al-Saidi, 2022 Image encryption based on local fractional derivative complex logistic map. Symmetry 14: 1874, 2022.
3. Hadeler, K. P., 2012 Pair formation. Journal of mathematical biology 64: 613–645.
4. Iannelli, M. M., Mimmo and F. A. Milner, 2005 Gender-structured population modeling: mathematical methods, numerics, and simulations. Society for Industrial and Applied Mathematics.
5. Kendall, D. G., 1997 Stochastic processes and population growth. Journal of the Royal Statistical Society 11: 230–282.
6. Keyfitz, H. C., N., 2005 Applied Mathematical Demography. Springer New York, NY.
7. Li, H. L.-Y. M. W. M. M. G. M., Ye Xuan and J. Y. Ma, 2022 Population dynamic study of prey-predator interactions with weak allee effect, fear effect, and delay. Journal of Mathematics 2022: 1–15.
8. Murty, P. A., K. and V. Prasannam, 1997 First order difference system-existence and uniqueness. Proceedings of the American Mathematical Society 125: 3533–3539.

9. N. M. Al-Saidi, D. B. R. W. I., H. Natiq, 2023 The dynamic and discrete systems of variable fractional order in the sense of the lozi structure map. AIMS Mathematics 8: 1–20.
10. Pollard, J. H., 1997 Modelling the interaction between the sexes. Mathematical and Computer Modelling 26: 11–24.
11. Rending L., M. W. F. A. K. F. N. M. A.-S., Balamurali R. and V.-T. P., 2022 Synchronization and different patterns in a network of diffusively coupled elegant wang–zhang–bao circuits. The European Physical Journal Special Topics 231: 3987–3997.
12. Salih, S. H. and N. Al-Saidi, 2022 3d-chaotic discrete system of vector borne disease using environment factor with deep analysis. AIMS Mathematics 7: 3972–3987.
13. Schoen, R., 2013 Modeling multigroup populations. Springer New York, NY.
14. Shaw, H. K., Allison K. and M. G. Neubert, 2018 Sex difference and allee effects shape the dynamics of sex-structured invasions. Journal of Animal Ecology 87: 36–46.
15. Waldstatter, R., 1989 Pair formation in sexually-transmitted diseases. Mathematical and statistical approaches to AIDS epidemiology pp. 260–274.
16. Yellin, J. and P. A. Samuelson, 1974 A dynamical model for human population. Proceedings of the National Academy of Sciences 71: 2813–2817.