| Contents |
| A dissipative Hopf - Hopf bifurcation with 2:1 resonance are studied. A parameter dependent polynomial truncated normal form is derived. We study this truncated normal form (TNF system). This system displays a large variety of behaviour both regular and chaotic solution. Existence of the stationary and periodic solutions is proved. The stationary and periodic solutions of TNF will correspond with periodic solutions and two dimensional torus of the original system. The occurrence of chaos in the TNF is studied. It is shown that the chaotic dynamics of TNF can be described in terms of bimodal one dimensional map. Analogy between dissipative Hopf - Hopf bifurcation with 2:1 resonance, generations of second harmonics in non-linear optics and resonant interaction of waves in a plasma is presented. |
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