Third-order resonance networks and their application to chaos generation

In this work, we re-visit third-order RLC resonance networks depicting the set of four basic series and parallel resonance circuits where two circuits are admittance based (parallel resonance) and the other two are impedance-based (series resonance). We show that all circuits exhibit resonance at a single frequency and derive its expression. However, all circuits also have another below-resonance or above-resonance critical frequency at which the input impedance (or admittance) is zero. We call this frequency, the dip-frequency and a change in phase also occurs at this frequency. Therefore, the third-order resonance networks exhibit two phase changes: one at the resonance frequency and another at the dip frequency. An application in realizing third-order non-autonomous chaotic oscillators is described and experimental results are provided.