Thermodynamic and Mechanic Consideration on the stability of Anti-symmetric Schaefer's equation

Abstract

Schaefer's equation relates an interaction between population of fishes and the number of units of fishing effort. The population growth of fishes is reduced by the number of units of fishing effort, while the population growth of units of fishing effort depends on the existence of fishes. This paper aims to examine the stability of an anti-symmetric Schaefer's equation through thermodynamic and mechanic procedure using a formula of entropy production near equilibrium which is recognized as Onsager's relation. The results confirm that entropic approach (thermodynamics) and dissipative approach (mechanics) are usable to be applied as Lyapunov's procedure in examining the stability of systems of differential equations.

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