Study of Lotka–Volterra Biological or Chemical Oscillator Problem Using the Normalization Technique: Prediction of Time and Concentrations

Juan Francisco Sánchez-Pérez, Manuel Conesa, Iván Alhama and Manuel Cánovas
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Juan Francisco Sánchez-Pérez: Department of Applied Physics, Universidad Politécnica de Cartagena, 30203 Cartagena, Spain
Manuel Conesa: Department of Applied Physics, Universidad Politécnica de Cartagena, 30203 Cartagena, Spain
Iván Alhama: Department of Mining and Civil Engineering, Universidad Politécnica de Cartagena, 30203 Cartagena, Spain
Manuel Cánovas: Department of Metallurgical and Mining Engineering, Universidad Católica del Norte, Antofagasta 1240000, Chile

Mathematics, 2020, vol. 8, issue 8, 1-16

Abstract: The normalization of dimensionless groups that rule the system of nonlinear coupled ordinary differential equations defined by the Lotka–Volterra biological or chemical oscillator has been derived in this work by applying a normalized nondimensionalization protocol. The normalization procedure, which is quite accurate, does not require complex mathematical steps; however, a deep physical understanding of the problem is required to choose the appropriate references to define the dimensionless variables. From the dimensionless groups derived, the functional dependences of some unknowns of interest are established. Due to the coupled nature of the problem that induces temporal concentration rates of each species that are quite different at each point of the phase diagram, this diagram has been divided into four stretches corresponding to the four quadrants. For each stretch, the limit values (maximum or minimum) of the variables, as well as their duration, are expressed in terms of the dimensionless groups derived before. Finally, to check all the mentioned dependences, a numerical simulation has been carried out.

Keywords: Lotka–Volterra oscillator; non-dimensionalization; dimensionless groups; numerical simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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