Stability Analysis of a Lotka-Volterra Type Biological Model in Its Fractional Version

Fabián Toledo Sánchez, Alex Raimundo Sepúlveda Cerda, Pedro Pablo Cárdenas Alzate


The stability of systems of ordinary differential equations of fractional order has been a study subject over the last two decades within fractional analysis. This study presented some fundamental results on the stability of linear fractional systems, which has allowed, in a certain sense, the generalization of some results for nonlinear fractional differential equations. This paper aims to present the fundamental results of the stability of systems of nonlinear ordinary differential equations of fractional order. These results are specified and demonstrated for a particular type of nonlinear differential equations of fractional order and applied to the analysis of the dynamics of a Lotka–Volterra-type biological model, which allows an analysis of the interaction between three species, some acting as prey and others as predator. The stability analysis of the prey–predator biological model used fractional operators in the sense of Caputo, and simulations verified these results.


Keywords: fractional calculus, fractional differential equations, stability of fractional differential equations, biological models, Lotka-Volterra type model.

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