18 research outputs found

    Resonance and frequency-locking phenomena in spatially extended phytoplankton-zooplankton system with additive noise and periodic forces

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    In this paper, we present a spatial version of phytoplankton-zooplankton model that includes some important factors such as external periodic forces, noise, and diffusion processes. The spatially extended phytoplankton-zooplankton system is from the original study by Scheffer [M Scheffer, Fish and nutrients interplay determines algal biomass: a minimal model, Oikos \textbf{62} (1991) 271-282]. Our results show that the spatially extended system exhibit a resonant patterns and frequency-locking phenomena. The system also shows that the noise and the external periodic forces play a constructive role in the Scheffer's model: first, the noise can enhance the oscillation of phytoplankton species' density and format a large clusters in the space when the noise intensity is within certain interval. Second, the external periodic forces can induce 4:1 and 1:1 frequency-locking and spatially homogeneous oscillation phenomena to appear. Finally, the resonant patterns are observed in the system when the spatial noises and external periodic forces are both turned on. Moreover, we found that the 4:1 frequency-locking transform into 1:1 frequency-locking when the noise intensity increased. In addition to elucidating our results outside the domain of Turing instability, we provide further analysis of Turing linear stability with the help of the numerical calculation by using the Maple software. Significantly, oscillations are enhanced in the system when the noise term presents. These results indicate that the oceanic plankton bloom may partly due to interplay between the stochastic factors and external forces instead of deterministic factors. These results also may help us to understand the effects arising from undeniable subject to random fluctuations in oceanic plankton bloom.Comment: Some typos errors are proof, and some strong relate references are adde

    The Date of Kanishka since 1960

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    The 1960 London Conference on the Date of Kanishka involved many leading scholars of Central and South Asian studies and had a profound impact on the field. This article examines the historiography of the central problem posed at the conference: In what year did the era of Kanishka commence? It traces the advances in evidence that led to the solution of AD 127 between 2000 and 2010. The complexity of this process is often omitted in historiographical accounts, which opens the final solution to criticism and also fails to address why the field polarised after 1960 and found it so hard to reconcile new evidence. The article suggests that the eventual solution was a result of the cumulative effect of new data. It also shows that the field as a whole arrived at a solution long before it arrived at a consensus. This suggests that the failure of new evidence to bring about a solution more quickly is a major challenge to South and Central Asian studies in the future
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