A Quadratic System with a Nonmonotonic Period Function
Copyright policy )A Quadratic System with a Nonmonotonic Period Function
For a certain c ∗ > 1.4 {c_ * } > 1.4 and c ∈ ( 1.4 , c ∗ ) c \in \left ( {1.4,{c_ * }} \right ) the quadratic system x ˙ = − y + x y , y ˙ = x + 2 y 2 − c x 2 \dot x = - y + xy,\dot y = x + 2{y^2} - c{x^2} has a center at the origin surrounded by a one-parameter family of periodic trajectories. We show the period is not a monotone function of the parameter.
Local and nonlocal bifurcation theory for dynamical systems, center, Nonlinear oscillations and coupled oscillators for ordinary differential equations, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, periodic trajectories, Periodic solutions to ordinary differential equations
Local and nonlocal bifurcation theory for dynamical systems, center, Nonlinear oscillations and coupled oscillators for ordinary differential equations, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, periodic trajectories, Periodic solutions to ordinary differential equations
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