Isolated resonances in a Dynamical System can cause considerable distortion of preserved Tori in their Neighborhood, but they do not introduce any Chaos into a system. However, when two or more resonances are simultaneously present, they will render a system nonintegrable. Furthermore, if they are sufficiently ``close'' to each other, they will result in the appearance of widespread (large-scale) Chaos.
To investigate this problem, Walker and Ford (1969) took the integrable Hamiltonian
Walker and Ford (1969) were able to numerically predict the energy at which the overlap of the resonances first occurred. They plotted the -axis intercepts of the inner 2:2 and the outer 2:3 separatrices as a function of total energy. The energy at which they crossed was found to be identical to that at which 2:2 and 2:3 resonance zones began to overlap.
See also Chaos, Resonance Overlap Method
References
Walker, G. H. and Ford, J. ``Amplitude Instability and Ergodic Behavior for Conservative Nonlinear Oscillator
Systems.'' Phys. Rev. 188, 416-432, 1969.