A Single Recurrence Simulates Growth Cycles in Nature

Alexander Harrison¹

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.8 , pp.1-7, Aug-2021

Online published on Aug 31, 2021

Copyright © Alexander Harrison . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Numerous systems in nature grow or decay over time, with many exhibiting cycloidal or S-shaped trajectories. Competing effects within any predator-prey system may lead to oscillatory and even chaotic trajectories. Natural systems including solar cycles and even ethanol production curves exhibit an S-curve trajectory during the growth cycle. Traditionally, differential equations are required to analyse the dynamics of a large system of distributed particles. An alternative method for describing growth paths in natural systems applies a single modulated discrete-domain recurrence relation to emulate the shape of growth or decay trajectories. The model requires a known initial condition and a growth target value for the particular physical system. Addition of a modulating term within the recursion model enables wave action within growth cycles, without impacting numerical simulation stability. A recurrence relation is developed to simulate the known growth and decay characteristics in real systems such as hurricanes, tornados, ethanol production during fermentation, coronavirus growth, solar cycle count and sunspot dynamics, to mention a few. Simulation by recursion of growth curves for the above-mentioned natural systems each show S-shape appearance, suggesting that systems with limiting growth may also submit to trajectory predictability. Growth curves for any physical systems that evolve from a minimum to a maximum value are amenable to analysis by the recurrence method.

Key-Words / Index Term :
Simulation, Dynamics, Recurrence, Nature, Growth, Decay

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