Bipolar (BI) Disorder (BD) is modelled using limit cycle oscillators, which characterizes its alternating nature: (Pure) (Hypo) Mania (PME) and Depressive Episodes (DE). Also, it is presented, within the mathematical framework designed by René Thom (Catastrophes Theory), the differentiation between BI structures-PME and Dipolar ones (DI)-Mixed Mania/Episode (ME). This differentiation is re-analysed through Ilya Prigogine thermodinamic construct scope of oscillatory systems, with strong fluctuations, and consecutive, emerging, accordingly to chaotic attractors, bifurcated structures. The results, even, at a clinical level, point to different mechanisms underlying BI and DI [PME responds to Lithium Therapy (Lt), contrasting with the poorer response to Lt revealed by Rapid Cycling, ME (and for instances, ethanol withdrawal seizures), which respond to agents that decrease - by quenching (through LTD), even, previously, kindled (through LTP) - the excitability of the implicated brain circuitries (such as anticonvulsive agents, rTMS). It is presented a model of the oscillatory character of NMDA glutamatergic system, within both contexts: BD/BI and ME/DI. in conclusion - detaining PME and ME different conceptual/biophysical, clinical and genetic foundations - it is proposed a revision of the worldwide classifications of Mental Disorders (DSM, ICD), concerning PME versus ME.