TY - JOUR

T1 - Birth of limit cycles for a class of continuous and discontinuous differential systems in (d + 2)–dimension

AU - Llibre, Jaume

AU - Teixeira, Marco A.

AU - Zeli, Iris O.

PY - 2016/7/2

Y1 - 2016/7/2

N2 - © 2015 Taylor & Francis. The orbits of the reversible differential system ẋ= − y, ẏ = x, ż = 0, with x, y ∈ R and z ∈ R d , are periodic with the exception of the equilibrium points (0, 0, z 1 ,… , z d ). We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system ẋ= − y, ẏ = x, ż = 0 , using the averaging theory of first order, when this system is perturbed, first inside the class of all polynomial differential systems of degree n, and second inside the class of all discontinuous piecewise polynomial differential systems of degree n with two pieces, one in y > 0 and the other in y < 0. In the first case, this maximum number is n d (n − 1)/2, and in the second, it is n d + 1 .

AB - © 2015 Taylor & Francis. The orbits of the reversible differential system ẋ= − y, ẏ = x, ż = 0, with x, y ∈ R and z ∈ R d , are periodic with the exception of the equilibrium points (0, 0, z 1 ,… , z d ). We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system ẋ= − y, ẏ = x, ż = 0 , using the averaging theory of first order, when this system is perturbed, first inside the class of all polynomial differential systems of degree n, and second inside the class of all discontinuous piecewise polynomial differential systems of degree n with two pieces, one in y > 0 and the other in y < 0. In the first case, this maximum number is n d (n − 1)/2, and in the second, it is n d + 1 .

KW - Limit cycle

KW - averaging method

KW - discontinuous polynomial differential systems

KW - periodic orbit

KW - polynomial differential system

UR - https://ddd.uab.cat/record/169449

U2 - https://doi.org/10.1080/14689367.2015.1102868

DO - https://doi.org/10.1080/14689367.2015.1102868

M3 - Article

VL - 31

SP - 237

EP - 250

JO - Dynamical Systems

JF - Dynamical Systems

SN - 1468-9367

IS - 3

ER -