Heterogeneity of neuronal properties determines the collective behavior of the neurons in the suprachiasmatic nucleus.

Circadian rhythms have been observed in behavioral and physiological activities of living things exposed to the natural 24 h light-darkness cycle. Interestingly, even under constant darkness, living organisms maintain a robust endogenous circadian rhythm suggesting the existence of an endogenous clock. In mammals, the endogenous clock is located in the suprachiasmatic nucleus (SCN) which is composed of about 20,000 neuronal oscillators. These neuronal oscillators are heterogeneous in their properties, including the intrinsic period, intrinsic amplitude, light information sensitivity, cellular coupling strength, intrinsic amplitudes and the topological links. In this review, we introduce the influence of the heterogeneity of these properties on the two main functions of the SCN, i.e. the free running rhythm in constant darkness and entrainment to the external cycle, based on mathematical models where heterogeneous neuronal oscillators are coupled to form a network. Our findings show that the heterogeneities can alter the free running periods under constant darkness and the entrainment ability to the external cycle for the SCN by controlling a fine balance between flexibility and robustness of the clock. These findings can explain experimental observation, e.g., why the free running periods and entrainment abilities are different between species, and shed light on the heterogeneity of the SCN network.

Onset of cooperation between layered networks.

Functionalities of a variety of complex systems involve cooperations among multiple components; for example, a transportation system provides convenient transfers among airlines, railways, roads, and shipping lines. A layered model with interacting networks can facilitate the description and analysis of such systems. In this paper we propose a model of traffic dynamics and reveal a transition at the onset of cooperation between layered networks. The cooperation strength, treated as an order parameter, changes from zero to positive at the transition point. Numerical results on artificial networks as well as two real networks, Chinese and European railway-airline transportation networks, agree well with our analysis.