A Second Order Solution of a Lotka-Volterra Model Near its Equilibrium Point.

Lotka-Volterra model continues to be of interest to numerous researchers, both in terms of its mathematical development and applications. This paper discusses an analytical solution of the Lotka-Volterra model near its equilibrium point. This solution, which is the main result of this paper, has not been previously explored by other researchers. The proposed solution is in the form of a series expansion with respect to parameter (1), representing a perturbed solution around the equilibrium point. The analytical solution is evaluated by comparing to both the corresponding exact orbit, which is directly derived from the model, and the corresponding numerical solution. Comparisons with the exact orbit reveal that the orbit formed by the analytical solution closely approximates the exact one. The orbits formed by the analytical solution are closer to the exact ones as approaches zero. Similarly, the analytical solution is also closer to the numerical solution as approaches zero. Additionally, as the solutions exhibit wave-like behavior, further observations are made regarding the 'amplitude' and 'wavelength' of the analytical solution. The wavelength and amplitude of the analytical solutions are closer to the ones of the numerical solutions as tends to zero. The amplitude and wavelength are crucial for optimizing harvesting strategies when applying the Lotka-Volterra model in integrated farming systems. [ABSTRACT FROM AUTHOR]