These dragonfly-like patterns are chaotic and quasi-periodic states in a radio-physical oscillator system. In their recent JPhysA paper, Kuznetsov and colleagues have investigated where these dynamics appear in a system that doesn’t have an equilibrium point, where one wouldn’t naturally expect to find this type of behaviour.
Figure: 2D projection of phase portraits of three co-existing hidden attractors in a radio-physical oscillator system, from A P Kuznetsov et al 2015 J. Phys. A: Math. Theor. 48 125101.