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Abstract: In this paper, control of Hopf bifurcation for a plankton population model with a non-integer exponent of closure is studied. For the plankton model with the closure term varies continuously between the commonly used linear and quadratic forms, washout filter aided feedback controllers are employed to control the stability of the Hopf bifurcation, and thus the chaos could be eliminated. By employing the stability theorems derived, the stability of a control system is investigated. Finally numerical simulations are provided to show the effectiveness and feasibility of the developed methods. [Copyright &y& Elsevier]

In Europe there is an extensive history of the derivation and use of benthic indicators which parallels similar developments in North America and elsewhere. Most recently, this has increased because major European Union Directives require that indicators of marine benthic change are used to confirm good ecological status quality (as in the Water Framework Directive) and favourable conservation status (as in the Habitats and Species Directive). Furthermore, these indicators have to fit within the current philosophy of the Ecosystem Approach requiring the development and use of Ecological Quality Objectives and Standards. Despite this, comparisons of families of indicators derived by differing methods have not been carried out such that the robust nature of the indicators on differing spatial scales and under differing benthic conditions has not been rigorously assessed. Using case studies from the Portuguese coasts and estuaries, this paper compares and contrasts univariate and multivariate macrobenthic indicators to quantify comparisons of change. The studies indicate the relative value of those indicators at contrasting spatial scales, e.g. in the transition from small areas around coastal submarine outfalls, to the local and regional estuarine and coastal scale. The analysis indicates the difficulties of deriving and using qualitative and quantitative indicators from benthic communities in stable, and in moderately and highly variable environmental conditions in estuarine, coastal and open sea habitats. In some areas, the variability in the indicators and indices within a station and site is as large as that between stations and sites. For those areas studied, there is an adequate quality and quantity of benthic data available for making management decisions but this is unlikely to be the case for all areas. Similarly, the interrogation of the methods shows that while their use and interpretation rely on a good understanding of the biology of the individual species and their responses to physical and polluting stress, that understanding is not yet available for many of the species. Most notably, while the indices and integrative indicators are becoming increasingly sophisticated, many are still dependent on the Pearson–Rosenberg model for organic enrichment hence they require to be validated for physical disturbance and for chemical pollution. Because of these features, the outcome of the analysis has repercussions for the management of coastal and estuarine areas. Although the present study indicates the value of indicators of benthic change for making management decisions at the various scales, further validation is required especially, for example, where one indicator over-estimates the ecological status for poor areas and underestimates it for good areas. [Copyright &y& Elsevier]