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1 – 2 of 2Chems Eddine Berrehail and Amar Makhlouf
The objective of this work is to study the periodic solutions for a class of sixth-order autonomous ordinary differential equations
Abstract
Purpose
The objective of this work is to study the periodic solutions for a class of sixth-order autonomous ordinary differential equations
Design/methodology/approach
The authors shall use the averaging theory to study the periodic solutions for a class of perturbed sixth-order autonomous differential equations (DEs). The averaging theory is a classical tool for the study of the dynamics of nonlinear differential systems with periodic forcing. The averaging theory has a long history that begins with the classical work of Lagrange and Laplace. The averaging theory is used to the study of periodic solutions for second and higher order DEs.
Findings
All the main results for the periodic solutions for a class of perturbed sixth-order autonomous DEs are presenting in the Theorem 1. The authors present some applications to illustrate the main results.
Originality/value
The authors studied Equation 1 which depends explicitly on the independent variable t. Here, the authors studied the autonomous case using a different approach.
Details
Keywords
In this article, the author discusses dynamical behaviors of a prey-predator population model with nonlinear harvesting rate and offers a mathematical analysis of the model.
Abstract
Purpose
In this article, the author discusses dynamical behaviors of a prey-predator population model with nonlinear harvesting rate and offers a mathematical analysis of the model.
Design/methodology/approach
The design is by using modelization of populations interaction, qualitative theory of ordinary différential equations, bifurcations analysis, invariant center manifolds theory and Dulac's criterion.
Findings
The author studies the stability of solutions and the existence of periodic solutions in the model, and proves the existence of some invariant sets and the production of a transcritical together with a saddle-node bifurcation.
Practical implications
The author studies the effects of harvesting on the persistence and extinction properties and its influence in the perspectives of economic views.
Originality/value
The authors considers a predator–prey model with a new nonlinear form of harvesting rate. The author’s intention is to make conceptual adjustments to a well-known predator–prey model in order to incorporate the effects of harvesting.
Details