Abstract. All the accessible auroral observations recorded in Chinese and Japanese histories during the interval AD 1840-1911 are investigated in detail. Most of these auroral records have never been translated into a Western language before. The East Asian auroral reports provide information on the date and approximate location of each auroral observation, together with limited scientific information on the characteristics of the auroral luminosity such as colour, duration, extent, position in the sky and approximate time of occurrence. The full translations of the original Chinese and Japanese auroral records are presented in an appendix, which contains bibliographic details of the various historical sources. (There are no known reliable Korean observations during this interval.) A second appendix discusses a few implausible "auroral" records, which have been rejected. The salient scientific properties of all exactly dated and reliable East Asian auroral observations in the interval AD 1840-1911 are summarised succinctly. By comparing the relevant scientific information on exactly dated auroral observations with the lists of great geomagnetic storms compiled by the Royal Greenwich Observatory, and also the tabulated values of the Ak (Helsinki) and aa (Greenwich and Melbourne) magnetic indices, it is found that 5 of the great geomagnetic storms (aa>150 or Ak>50) during either the second half of the nineteenth century or the first decade of the twentieth century are clearly identified by extensive auroral displays observed in China or Japan. Indeed, two of these great storms produced auroral displays observed in both countries on the same night. Conversely, at least 29 (69%) of the 42 Chinese and Japanese auroral observations occurred at times of weak-to-moderate geomagnetic activity (aa or Ak≤50). It is shown that these latter auroral displays are very similar to the more numerous (about 50) examples of sporadic aurorae observed in the United States during the interval AD 1880-1940. The loCorrespondence to: D. M. Willis (d.m.willis@rl.ac.uk) calised nature and spatial structure of some sporadic aurorae observed in East Asia is indicated by the use of descriptive terms such as "lightning", "rainbow", "streak" and "grid".

In this paper, we study the solution of impulsive fractional differential equations with multiple delays by using the nonlinear alternative of Leray-Schauder and the Banach fixed point method. Also, we prove that the equations have at least one solution or unique solution with certain conditions. In the last part, we give two examples to illustrate the usefulness of the main results.

This paper mainly aims to consider the dynamical behaviors of a diffusive delayed predator–prey system with Smith growth and herd behavior subject to the homogeneous Neumann boundary condition. For the analysis of the predator–prey model, we have studied the existence of Hopf bifurcation by analyzing the distribution of the roots of associated characteristic equation. Then we have proved the stability of the periodic solution by calculating the normal form on the center of manifold which is associated to the Hopf bifurcation points. Some numerical simulations are also carried out in order to validate our analysis findings. The implications of our analytical and numerical findings are discussed critically.

Abstract. This paper discusses the nonlinear dynamics of Shen-Larter calcium oscillation model with the center manifold theorem and bifurcation theory. A numerical approach is provided to discuss the variation in classification and stability of equilibria with parameter value. It is shown that the critical values of parameter in this model are due to supercritical Hopf bifurcation of equilibria. This numerical simulation confirms the theoretical results of this research. Finally, a complete description of the complex dynamics of the Shen-Larter calcium oscillation model is provided by combining the numerical and theoretical results.

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