In healthy humans and other animals, behavioral activity exhibits scale invariance over multiple timescales from minutes to 24 h, whereas in aging or diseased conditions, scale invariance is usually reduced significantly. Accordingly, scale invariance can be a potential marker for health. Given compelling indications that exercise is beneficial for mental and physical health, we tested to what extent a lack of exercise affects scale invariance in young and aged animals. We studied six or more mice in each of four age groups (0.5, 1, 1.5, and 2 y) and observed an age-related deterioration of scale invariance in activity fluctuations. We found that limiting the amount of exercise, by removing the running wheels, leads to loss of scale-invariant properties in all age groups. Remarkably, in both young and old animals a lack of exercise reduced the scale invariance in activity fluctuations to the same level. We next showed that scale invariance can be restored by returning the running wheels. Exercise during the active period also improved scale invariance during the resting period, suggesting that activity during the active phase may also be beneficial for the resting phase. Finally, our data showed that exercise had a stronger influence on scale invariance than the effect of age. The data suggest that exercise is beneficial as revealed by scale-invariant parameters and that, even in young animals, a lack of exercise leads to strong deterioration in these parameters.

Information spreading has been studied for decades, but its underlying mechanism is still under debate, especially for those ones spreading extremely fast through the Internet. By focusing on the information spreading data of six typical events on Sina Weibo, we surprisingly find that the spreading of modern information shows some new features, i.e., either extremely fast or slow, depending on the individual events. To understand its mechanism, we present a susceptible-accepted-recovered model with both information sensitivity and social reinforcement. Numerical simulations show that the model can reproduce the main spreading patterns of the six typical events. By this model, we further reveal that the spreading can be speeded up by increasing either the strength of information sensitivity or social reinforcement. Depending on the transmission probability and information sensitivity, the final accepted size can change from continuous to discontinuous transition when the strength of the social reinforcement is large. Moreover, an edge-based compartmental theory is presented to explain the numerical results. These findings may be of significance on the control of information spreading in modern society.

The suprachiasmatic nucleus (SCN) pacemaker shows a free-running period ranging from 20 to 28 h for different species, which was usually explained from the angle of coupling strength. Based on the assumption of nonidentical coupling strengths in SCN, we find an alternative mechanism that the diversity of free-running period can be also caused by the distribution of coupling strengths. The free-running period is proportional to the average coupling strength and inverse proportional to the dispersion of couplings. Moreover, we present an analytic phase model to confirm our finding, which shows a solid foundation of our finding and opens a window to study the collective behaviors of SCN oscillators.

The dominant endogenous clock, named the suprachiasmatic nucleus (SCN), regulates circadian rhythms of behavioral and physiological activity in mammals. One of the main characteristics of the SCN is that the animal maintains a circadian rhythm with a period close to 24 h in the absence of a daily light-dark cycle (called the free running period). The free running period varies among species due to heterogeneity of the SCN network. Previous studies have shown that the heterogeneity in cellular coupling as well as in intrinsic neuronal periods shortens the free running period. Furthermore, as derived from experiments, one neuron's coupling strength is negatively associated with its period. It is unknown what the effects of this association between coupling strength and period are on the free running period and how the heterogeneity in coupling strength influences this free running period. In the present study we found that in the presence of a negative relationship between one neuron's coupling strength and its period, surprisingly, the dispersion of coupling strengths increases the free running period. Our present finding may shed new light on the understanding of the heterogeneous SCN network and provides an alternative explanation for the diversity of free running periods between species.

The suprachiasmatic nucleus (SCN) is a principal circadian clock in mammals, which controls physiological and behavioral daily rhythms. The SCN has two main features: Maintaining a rhythmic cycle of approximately 24 h in the absence of a light-dark cycle (free-running period) and the ability to entrain to external light-dark cycles. Both free-running period and range of entrainment vary from one species to another. To understand this phenomenon, we investigated the diversity of a free-running period by the distribution of coupling strengths in our previous work [Phys. Rev. E 80, 030904(R) (2009)]. In this paper we numerically found that the dispersion of intrinsic periods among SCN neurons influence the entrainment range of the SCN, but has little influence on the free-running periods under constant darkness. This indicates that the dispersion of coupling strengths determines the diversity in free-running periods, while the dispersion of intrinsic periods determines the diversity in the entrainment range. A theoretical analysis based on two coupled neurons is presented to explain the results of numerical simulations.

The phase-splitting behavior of coupled suprachiasmatic-nucleus neurons has been observed in many mammals, and its mechanism is still not completely understood. Based on our previous work [C. Gu, J. Wang, and Z. Liu, Phys. Rev. E 80, 030904(R) (2009)] on the free-running periods of neurons in the suprachiasmatic nucleus, we present here a modified Goodwin oscillator model to explain the mechanism of phase splitting. In contrast to the previous phase model, the modified Goodwin oscillator model contains the information on both the phase and amplitude and, thus, can show more features than the purely phase model, including all three behaviors of synchronization, phase splitting, and amplitude death and the distributed periodicity in the regions of synchronization and phase splitting, etc. An analytic phase model is extracted from the modified Goodwin oscillator model to explain the dependence of periodicity on the parameters. Moreover, both the modified Goodwin oscillator model and the analytic phase model show that the ensemble frequency can be enhanced or reduced by the time delay.