Serotonin, dopamine and norepinephrine are monoamine neurotransmitters that modulate our mood state. Hence, imbalances in the levels of these neurotransmitters have been linked to the incidence of several psychiatric disorders. Here, a mathematical model written in terms of ordinary differential equations is proposed to represent the interaction of these three neurotransmitters. It is analytically and numerically shown that this model can experience a Hopf bifurcation. Thus, by varying a parameter value, the neurotransmitter levels can change from a steady state to an oscillatory behavior, which may be at least a partial explanation of the mood swings observed in depressed people.
Keywords: Hopf bifurcation; dopamine; dynamical system; mood instability; norepinephrine; serotonin.