On boundedness of solutions of quadratic differential equation sets

V.Ye. Belozerov; V.S. Chernyshenko; S.V. Chernyshenko

doi:10.15421/240706

On boundedness of solutions of quadratic differential equation sets

V.Ye. Belozerov (Dnipropetrovsk National University), https://orcid.org/0000-0003-2888-8876
V.S. Chernyshenko (Dnipropetrovsk National University)
S.V. Chernyshenko (Dnipropetrovsk National University), https://orcid.org/0000-0002-2852-6878

Abstract

We obtain new sufficient conditions of asymptotic stability on solution cone of the set of usual uniform quadratic differential equations. For non-uniform quadratic sets (with non-zero linear part) we give the conditions of boundedness of solutions. We determine quadratic sets whose solution is bounded for any linear part and for any initial conditions. We provide examples of applications of the method in mathematical ecology.

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