Displaying similar documents to “Attractors with vanishing rotation number”

Dynamics of a Lotka-Volterra map

Francisco Balibrea, Juan Luis García Guirao, Marek Lampart, Jaume Llibre (2006)

Fundamenta Mathematicae

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Given the plane triangle with vertices (0,0), (0,4) and (4,0) and the transformation F: (x,y) ↦ (x(4-x-y),xy) introduced by A. N. Sharkovskiĭ, we prove the existence of the following objects: a unique invariant curve of spiral type, a periodic trajectory of period 4 (given explicitly) and a periodic trajectory of period 5 (described approximately). Also, we give a decomposition of the triangle which helps to understand the global dynamics of this discrete system which is linked with...

The periodic problem for the second order integro-differential equations with distributed deviation

Sulkhan Mukhigulashvili, Veronika Novotná (2021)

Mathematica Bohemica

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We study the question of the unique solvability of the periodic type problem for the second order linear integro-differential equation with distributed argument deviation u ' ' ( t ) = p 0 ( t ) u ( t ) + ∫ 0 ω p ( t , s ) u ( τ ( t , s ) ) d s + q ( t ) , and on the basis of the obtained results by the a priori boundedness principle we prove the new results on the solvability of periodic type problem for the second order nonlinear functional differential equations, which are close to the linear integro-differential equations. The proved results are optimal in some...