Diffusion-driven instability is a basic nonlinear mechanism for pattern formation. Therefore, the way of population diffusion may play a determinative role in the spatiotemporal dynamics of biological systems. In this research, we launch an investigation on the pattern formation of a discrete predator-prey system where the population diffusion is based on the Moore neighborhood structure instead of the von Neumann neighborhood structure widely applied previously. Under pattern formation conditions which are determined by Turing instability analysis, numerical simulations are performed to reveal the spatiotemporal complexity of the system. A pure Turing instability can induce the self-organization of many basic types of patterns as described in the literature, as well as new spiral-spot and labyrinth patterns which show the temporally oscillating and chaotic property. Neimark-Sacker-Turing and flip-Turing instability can lead to the formation of circle, spiral and much more complex patterns, which are self-organized via spatial symmetry breaking on the states that are homogeneous in space and non-periodic in time. Especially, the emergence of spiral pattern suggests that spatial order can generate from temporal disorder, implying that even when the predator-prey dynamics in one site is chaotic, the spatially global dynamics may still be predictable. The results obtained in this research suggest that when the way of population diffusion changes, the pattern formation in the predator-prey systems demonstrates great differences. This may provide realistic significance to explain more general predator-prey coexistence.

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We present in this paper an investigation on a discrete predator-prey system with Crowley-Martin type functional response to know its complex dynamics on the routes to chaos which are induced by bifurcations. Via application of the center manifold theorem and bifurcation theorems, occurrence conditions for flip bifurcation and Neimark-Sacker bifurcation are determined, respectively. Numerical simulations are performed, on the one hand, verifying the theoretical results and, on the other hand, revealing new interesting dynamical behaviors of the discrete predator-prey system, including period-doubling cascades, period-2, period-3, period-4, period-5, period-6, period-7, period-8, period-9, period-11, period-13, period-15, period-16, period-20, period-22, period-24, period-30, and period-34 orbits, invariant cycles, chaotic attractors, sub-flip bifurcation, sub-(inverse) Neimark-Sacker bifurcation, chaotic interior crisis, chaotic band, sudden disappearance of chaotic dynamics and abrupt emergence of chaos, and intermittent periodic behaviors. Moreover, three-dimensional bifurcation diagrams are utilized to study the transition between flip bifurcation and Neimark-Sacker bifurcation, and a critical case between the two bifurcations is found. This critical bifurcation case is a combination of flip bifurcation and Neimark-Sacker bifurcation, showing the nonlinear characteristics of both bifurcations.Hindawi

PurposeWith the development of Web2.0 and publishing digitalization, traditional libraries and evaluation citation system can no longer indicate academic paper influence validly. Therefore, it is necessary to construct smart library and find the evaluation effect of Internet metrics-Usage.Design/methodology/approachThis study puts forward four indexes of scholars’ evaluation based on Usage (total Usage (U), average Usage rate (U/N), hu-index and pu-index), which refer to citation indexes, takes the 35 high-output scholars in the field of library and information science in the WoS database as examples, analyzes performance of different scholars evaluation indexes based on Usage and compares the differences and correlations between “citation indicators” and “usage indicators.”FindingsThis study results show that pu-index is the strongest index to evaluate scholars. Second, there is a high correlation and strong mechanism based on time dependence and interactions between Usage and citation. Third, compared to “citation indicators”, the “usage indicators” has a larger numerical value and wider measurement range, which can break the time limitation of citation, and scientifically evaluate young scholars and newly published paper by scholars.Originality/valueThis paper proposes the pu-index – a relatively superior mathematical model for Usage and provides reference for the scholars’ evaluation policy of the smart library. This model can not only provide fair evaluation conditions for young scientists but also shorten the evaluation effect of the time lag of cited indicators. In addition, the “usage indicators” in this paper are new scientific evaluation indicators generated in the network environment. Applying it to the academic evaluation system will make the research papers widely accepted by the public and will also encourage scientists to follow the development of the Internet age and pursue research with equal emphasis on quantity and quality.

The research on regular and irregular vegetation pattern formation in semiarid regions is an important field in ecology. Applying the framework of coupled map lattice, a novel nonlinear space- and time-discrete model is developed based on discretizing the classical Klausmeier model and the vegetation pattern formation in semiarid regions is restudied in this research. Through analysis of Turing-type instability for the discrete model, the conditions for vegetation pattern formation are determined. The discrete model is verified by Klausmeier’s results with the same parametric data, and shows advantages in quantitatively describing diverse vegetation patterns in semiarid regions, such as the patterns of regular mosaicirregular patches, stripes, fractured stripesspots, and stripes-spots, in comparing with former theoretical models. Moreover, the discrete model predicts variations of rainfall and vegetation types can cause transitions of vegetation patterns. This research demonstrates that the nonlinear mechanism of the discrete model better captures the diversity and complexity of vegetation pattern formation in semiarid regions.