An Analytic Solution to The Inhomogeneous Verhulst Equation Using Multiple Expansion Methods

Agus Salim (Department of Biology, Universitas Islam Negeri Syarif Hidayatullah, Jakarta-15412 (Indonesia))
Albert Sulaiman (Research Center for Climate and Atmosfer, Badan Riset dan Inovasi Nasional (BRIN), Bandung-40173 (Indonesia))
Mishima Kenji (Department of Chemical Engineering, Fukuoka University, Fukuoka-81401 (Japan))

Journal of Multidisciplinary Applied Natural Science
Vol. 3 No. 2 (2023): Journal of Multidisciplinary Applied Natural Science

The present study aims to obtain an analytic solution for the inhomogeneous Verhults equation using multiple expansion methods. This study identifies the external factors represented by the inhomogeneous term that determine optimal variable conditions for ecosystem population growth. The simulation involves scenarios that utilize constant growth rates, periodic growth rates, constant external factors, and periodic external factors. It is found that external factors increase population growth, whereas constant external factors prevent growth under saturation conditions. Periodic external factors cause fluctuations in the amplitude of growth regions. The present study will highlight and discuss the development and application of the solution.