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AbstractFor a stock market, a critical problem is the maintenance of its liquidity. Market liquidity can be described in various ways, in particular, in terms of the bid/offer spread and the market depth. A model of market liquidity dynamics has been proposed in the literature. In our study, we improve on this model. On the one hand, we think that trading volume is determined by the total number of traders, as well as the relations between the numbers of buyers and sellers, while the model of Schmidt only considered the first term. On the other hand, Schmidt assumes that the number of 'newcomers' in the market is in proportion to the current number of trades. However, we all know that the continual rising or decrease of the price will also attract more buyers or sellers, that is, 'newcomers', into the market, which Schmidt has not taken for granted. On the assumption that price variation can be neglected, we discuss the conditions in which chaos will emerge through analysis of the Lyapunov exponent. Finally, we implement a computer simulation of the model in MATLAB, and obtain more interesting results. Copyright © 2003 John Wiley & Sons, Ltd.

JWBR received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No. 805246) and from the Natural Environmental Research Council (NERC) grant NE/N011716/1. ; Boron isotopes in marine carbonates are increasingly used to reconstruct seawater pH and atmospheric pCO2 through Earth's history. While isotope ratio measurements from individual laboratories are often of high quality, it is important that records generated in different laboratories can equally be compared. Within this Boron Isotope Intercomparison Project (BIIP), we characterised the boron isotopic composition (commonly expressed in δ11B) of two marine carbonates: Geological Survey of Japan carbonate reference materials JCp‐1 (coral Porites) and JCt‐1 (giant clam Tridacna gigas). Our study has three foci: (a) to assess the extent to which oxidative pre‐treatment, aimed at removing organic material from carbonate, can influence the resulting δ11B; (b) to determine to what degree the chosen analytical approach may affect the resultant δ11B; and (c) to provide well‐constrained consensus δ11B values for JCp‐1 and JCt‐1. The resultant robust mean and associated robust standard deviation (s*) for un‐oxidised JCp‐1 is 24.36 ± 0.45‰ (2s*), compared with 24.25 ± 0.22‰ (2s*) for the same oxidised material. For un‐oxidised JCt‐1, respective compositions are 16.39 ± 0.60‰ (2s*; un‐oxidised) and 16.24 ± 0.38‰ (2s*; oxidised). The consistency between laboratories is generally better if carbonate powders were oxidatively cleaned prior to purification and measurement. ; Publisher PDF ; Peer reviewed