Due to the investigations carried out in neuroscience, it has been clear that basal ganglia circuits are not active only in motor actions but also take part in cognitive processes. With recent studies on processes as decision making and behavioral deficits as addiction, the role of basal ganglia in these processes has been revealed without suspicion. The activity in direct and indirect pathways, two of the three most mentioned pathways of basal ganglia, is known to be modified by neurotransmitter dopamine. In this work, a mathematical model will be derived which will reveal how the activity in the output component of basal ganglia circuit, globus pallidius externa and in the thalamus, which conveys information to the cortex, follows the activity of direct and indirect pathways modified by dopamine. While deriving the mathematical model, the activity in the structures forming the basal ganglia circuit is investigated through the neuron population activity obtained by point neurons. Firstly, the changes made in the single neuron model denoted by a dynamical system to obtain the neuronal activity of each structure is given. After these single neuron models, how each neuron population corresponding to basal ganglia structures is formed is explained and the simulation results obtained in BRIAN environment are discussed.