Pemodelan Matematika Berbasis Persamaan Diferensial Untuk Menganalisis Dinamika Pertumbuhan Populasi Dan Keseimbangan Ekosistem

Abstrak

Purpose: This article examines differential-equation-based mathematical models for explaining population growth and assessing ecosystem equilibrium under resource constraints and species interactions. Design/Methodology: A conceptual and analytical literature review compares exponential growth, logistic growth, Lotka–Volterra predator–prey dynamics, and functional-response extensions. The models are interpreted through equilibrium points, local stability, parameter sensitivity, and illustrative scenarios; no empirical field dataset is claimed.

Findings: Exponential growth represents an unconstrained baseline, whereas logistic dynamics introduce carrying capacity and a locally stable positive equilibrium under constant parameters. Predator–prey models reveal how interaction terms can produce oscillatory behavior; however, the classical Lotka–Volterra model is neutrally stable and does not, on its own, establish ecological resilience. Density dependence, functional responses, environmental variability, and observation uncertainty substantially affect interpretation. Practical Implications: The framework can guide biodiversity monitoring, conservation scenario design, ecological education, and transparent model evaluation, provided parameters are calibrated against appropriate observations and uncertainty is reported.

 Originality/Value: The article integrates mathematical equilibrium analysis with ecological interpretation and reproducibility requirements, highlighting the distinction between mathematical stability, persistence, and practical ecosystem resilience.