Modeling of Neurodegenerative Diseases Using Discrete Chaotic Systems

Parkinson's and Huntington's diseases are two of the most common neurodegenerative disorders. Tremor, muscle stiffness, and slowness of movement are symptoms of Parkinson's disease. The symptoms of Huntington's disease are severe reduction in muscle control, emotional disturbance, and pathological disorders in brain cells. These diseases are caused by destruction of the cells that secrete a substance called dopamine. In this paper, a new discrete chaotic system is introduced, which can mimic the brain's behavior for neurodegenerative diseases such as Parkinson, Huntington, and Hypokinesia. This system is described based on the similarity between the brain's behavior in normal and abnormal conditions and the chaotic systems. Bifurcation analysis is carried out with respect to different parameters, providing full spectrum of the behavior for different parameter values. Our results can be used to mathematically study the mechanisms behind these diseases.