Simulation of activity rhythms in the hamster

In this research, an effort was made to better understand light-dark cycles which influence the physiological and psychological rhythms, circadian rhythms and their behavior. The research concentrated on mathematically modeling circadian rhythms (specifically hamsters\u27 circadian activity rhythms) and establishing a physical correlation and creating a meaningful relationship between the mathematical model\u27s parameters and the real biological oscillators which are responsible for these rhythms. The internal nature of the circadian rhythms is unclear. There is insufficient information and empirical data that describe them. Indirect means have to be employed for the description and exploration of such rhythms. Extensive real data analysis must be performed in the time and frequency domains and every possible aspect of the circadian rhythms should be investigated. In our research, we studied and analyzed two types of circadian data, temperature and activity, which were extracted from rhesus monkeys and hamsters respectively by means of two separate data acquisition systems. The analysis which was accomplished in both the time and frequency domains revealed many important aspects of the circadian system and its characteristics. It was found that the circadian rhythms\u27 period is approximately 24 hours. This period showed a small deviation when the animal was subjected to different environmental conditions (light, food, etc.). The frequency spectrum of the real circadian data showed its harmonics structure and revealed the existence of two distinct frequency components (bimodality). Based on our analysis results and the knowledge of previous researchers work, we developed a nonlinear two coupled-oscillator mathematical model to approach the real circadian data. The numerical solutions of the model were obtained by computer simulation and were compared to the real circadian data in both the time and frequency domains. Certain modifications of the model were necessary to achieve the desired outcome. These modifications not only included the changes in the value of the model\u27s parameters, but also the addition of a high frequency oscillator. Later in the research, a periodic external stimulus was applied to the model in order to simulate entrainment. Our research has proven the ability of our mathematical model to simulate the circadian system