We analyzed the topological changes and the synchronization phenomena in a phase oscillators model, which reproduce qualitatively the experimental results about the behavior of mice under jet-lag conditions (recover from one abrupt change in the light input) for different levels of coupling between the neurons [1]. We considered a light input of one time zone for ld days and of another time zone for (7 - ld) days in order to emulate something analogous to the artificial light stimulus of people who suffer from social jet-lag. We found in the parameter space regions with bifurcations, bistability, period doubling and chaos, but in the majority of the space parameter the solutions are periodic. Also, due the high non-linearity of the model, in some specific regions of the parameter space there is a counter intuitive phenomenon: the individual spends more time in the week under a light stimulus A than B, and yet is better synchronized with the light stimulus B.

[1] Y. Yamaguchi, T. Suzuki, Y. Mizoro, H. Kori, K. Okada, Y. Chen, J.-M. Fustin, F. Yamazaki, N. Mizuguchi, J. Zhang, X. Dong, G. Tsujimoto, Y. Okuno, M. Doi, and H. Okamura, “Mice genetically deficient in vasopressin v1a and v1b receptors are resistant to jet lag”, Science 342, 85–90 (2013).