1. The problem statement, all variables and given/known data Does x' = xex2tanh(x+y) + (1/2)ex2sech2(x+y) y' = (1/2)ex2sech2(x+y) contain a limit cycle? Possibly-relevant theorem below. 2. Relevant equations Theorem. Closed orbits are impossible in gradient systems. Definition. If x' = -ΔV for some cont. diff'ble, single-valued scalar func. V(x), then such a system is called a gradient system with potential function V. 3. The attempt at a solution So the problem looks like a setup to apply this theorem .... but I can't figure out how. I've started at it for like 1 hr. Thanks in advance.