Phase locking in the circadian rhythm
Wijeratne, Nilmini Saumya
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Existence of an internal timing mechanism in mammals has been well established and known as the Circadian Rhythm which is generated in a bilateral structure contained in the hypothalamus called the Suprachaismatic Nucleus (SCN) which consists of 16,000 neurons. Individually, each neuron behaves like a clock, and the ensemble of neurons are capable of producing well-synchronized and phased-locked clock signals with precise time patterns. In this thesis, theory of Hopf Bifurcation in the presence of symmetries and the Center Manifold theory are used to explain the functionality and phase locking of the SCN. In addition, dynamical behavior of the system is simulated for different connection topologies and different bifurcation parameters. Also, system response in the presence of a second bifurcation parameter is also analyzed. Center Manifold theory describes a way to extract out a dynamical system representative of persistent dynamical effects. In order to compute the reduced order representative, the Taylor series expansion was incorporated into our work. Use of symmetries eliminates the necessity to calculate the Taylor series coefficients for all unstable states, thus reducing the calculations by a considerable amount.