Permanence and almost periodic solution of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales

In this paper, we consider the almost periodic dynamics of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales. By establishing some dynamic inequalities on time scales, a permanence result for the model is obtained. Furthermore, by means of the almost periodic functional hull theory on time scales and Lyapunov functional, some criteria are obtained for the existence, uniqueness and global attractivity of almost periodic solutions of the model. Our results complement and extend some scientific work in recent years. Finally, an example is given to illustrate the main results.Comment: 31page

Universal presence of time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators

In this work, we reported a ubiquitous presence of topological Floquet time crystal (TFTC) in one-dimensional periodically-driven systems. The rigidity and realization of spontaneous discrete time-translation symmetry (DTS) breaking in our model require necessarily coexistence of anomalous topological invariants (0 modes and $\pi$ modes), instead of the presence of disorders or many-body localization. We found that in a particular frequency range of the underlying drive, the anomalous Floquet phase coexistence between zero and pi modes can produce the period-doubling (2T, two cycles of the drive) that breaks the spontaneously, leading to the subharmonic response ($\omega/2$, half the drive frequency). The rigid period-oscillation is topologically-protected against perturbations due to both non-trivially opening of 0 and $\pi$-gaps in the quasienergy spectrum, thus, as a result, can be viewed as a specific "Rabi oscillation" between two Floquet eigenstates with certain quasienergy splitting $\pi/T$. Our modeling of the time-crystalline 'ground state' can be easily realized in experimental platforms such as topological photonics and ultracold fields. Also, our work can bring significant interests to explore topological phase transition in Floquet systems and to bridge the gap between Floquet topological insulators and photonics, and period-doubled time crystals.Comment: 31 pages, 6 figures, 2 supplementary figure

The Impact of Nonfarm Activities on Agricultural Productivity in Rural China

Although evidence abounds that the development of rural non-farm activities have increased rural household income and contributed to rural development, the underlying structure and mechanism of the linkage between agricultural productivity and non-farm activities is poorly understood. Using a unique panel dataset of Chinese villages, this article examines the mechanism by which non-farm activities influence agricultural productivity. I find that Chinese villages’ non-farm revenue has a significant positive effect on agricultural land productivity. Although non-farm activities do withdraw labor out of agriculture and therefore dampen land productivity, that negative effect is negligible in comparison with the land productivity improvement brought by nonfarm revenue-financed infrastructure capital investment.Rural non-farm activities, labor migration, agricultural productivity, infrastructure capital., Agricultural and Food Policy, Productivity Analysis, O13, Q18,