A Qualitative Study of a Trigonometric Autonomous System

A qualitative analysis is made of the autonomous system ẋ = sin y,ẏ = −sin x + d sin ny defined on the torus T2=[−π, π] × [−π, π], where d ∈ R and n is a positive integer. It is proved that for 0 < d ⪡ 1 the system has at least 2(n−1) limit cycles