Copied Prove that there exists a nonconstant periodic orbit. \[ \dot {x}=y \] \[ \dot {y}=-x+y(1-x^2-2y^2). \] Raw LaTeX Prove that there exists a nonconstant periodic orbit. \[ \dot{x}=y \] \[ \dot{y}=-x+y(1-x^2-2y^2). \] Topic Tags Periodic Orbits, Limit Cycles, and Orbital Stability Poincare Maps and Periodic Solutions