Chaotic behavior and controlling chaos in a fast-slow plankton-fish model

The interaction of different time scales in predator-prey models has become a common research topic. In the present article, we concentrated on the dynamics of interactions at two time scales in a plankton-fish system. To investigate the effects of the two time scales on plankton-fish dynamics, we constructed a new parameter with a corrected type that differs from the traditional slow parameter. In addition, zooplankton's refuge from the predator and phytoplankton mortality due to competition are incorporated into the model. Positivity and boundedness of solutions were proved. We then discussed feasibility and stability conditions of the equilibrium. We used a variety of means to support the existence of chaos in the system. Hopf bifurcation conditions were also obtained. Chaos control in the plankton-fish model is one of the main motivations for this study. In the slow-variable parameter case, we explored the control mechanism of gestation delay on chaotic systems, which are calmed by different periodic solutions. Moreover, under seasonal mechanisms, external driving forces can stabilize the system from chaos to periodic oscillations. Meanwhile, the sliding mode control (SMC) approach quickly calms chaotic oscillations and stabilizes it to an internal equilibrium state. The necessary numerical simulation experiments support the theoretical results

Dynamical Models of Biology and Medicine

Mathematical and computational modeling approaches in biological and medical research are experiencing rapid growth globally. This Special Issue Book intends to scratch the surface of this exciting phenomenon. The subject areas covered involve general mathematical methods and their applications in biology and medicine, with an emphasis on work related to mathematical and computational modeling of the complex dynamics observed in biological and medical research. Fourteen rigorously reviewed papers were included in this Special Issue. These papers cover several timely topics relating to classical population biology, fundamental biology, and modern medicine. While the authors of these papers dealt with very different modeling questions, they were all motivated by specific applications in biology and medicine and employed innovative mathematical and computational methods to study the complex dynamics of their models. We hope that these papers detail case studies that will inspire many additional mathematical modeling efforts in biology and medicin

Examples of Global and Regional Laws and Policies Relevant to Addressing the Potential Impacts of Climate Change and Ocean Acidification

Laws and policies relevant to the potential impacts of climate change and ocean acidification on marine species and coastal communities appear at the global and regional level, as well as the national level (see Annex 6)

Annex 6: Changing Ocean Impacts on the Key Forage Fish Species Arctic Cod in the Western Canadian Arctic – Linking Climate Model Projections to Subsistence Fisheries

This annex highlights the results of a study focusing on the potential impacts of ocean acidification and other climate- related stressors on marine species relevant for subsistence fisheries in the Western Arctic Bioregion. The study uses a knowledge co-production approach developed in the form of a multi-step process based on a combination of modelling and analysis tools including the Scientific Method and Indigenous Traditional Knowledge (Figure A6.1). Once all steps have been completed, uncertainties can be estimated and improvements can be made either with respect to the individual steps or to the linkages between them. The process can then be repeated, including those improvements to provide a revised assessment with reduced uncertainty ranges. The steps can be summarized as follows: (1) analyze past observed trends; (2) perform projection simulations with global and regional climate models, allowing trend estimates on 20–50 year timescales; (3) assess physiological responses and thresholds in marine species via literature research, Indigenous Traditional Knowledge, observations and focused laboratory experiments; (4) add trends, climate model projections and physiological response data to species distribution / habitat suitability and higher trophic level Ecosim/ Ecopath (see Section A6.3) models; (5) assess socio-economic impacts by applying bio-economic models, evaluating current fishery-economic activities, and discussion with communities/ community representatives; and (6) review law and governance. The latter addresses adaptation measures on global, regional and national scales. This annex describes the first application of the multi-step framework in the Western Arctic Bioregion. At this point in time all the required tools have been developed, but not all components have been adequately linked. For example, while higher resolution model projections are available for the area the habitat suitability and economic models are still driven by global climate models, the Ecopath model (see Section on The Beaufort Sea food web model) has not yet been run into the future and physiological responses are reflected in the higher trophic level models to a limited extent, if at all. In addition, while collaboration with local communities has been established (see Section on Community interests), Indigenous Traditional Knowledge has been included to a very limited extent. To summarize, this case study provides an assessment that includes all required tools, but limited linkages. It has a strong focus on uncertainty analyses and the identification of gaps in knowledge. Particular emphasis is given to the key forage fish species Arctic cod (Boreogadus saida), since climate model projections can be linked more directly to key forage species than to the (mostly) higher trophic level species harvested

Economic-Ecological Modeling

This book is about mathematical models for environmental and resource policy and management. The authors present an overview of the theory, methods, techniques, and experience relevant to the analysis of problems of the interface of society and its natural environment. They also evaluate the scientific adequacy and policy effectiveness of a wide variety of applied economic-ecological models. Furthermore, they indicate the reasons for success and failure of these model applications and summarize options for their improvement

Abstracts of papers submitted in 1978 for publication : Woods Hole Oceanographic Institution, Woods Hole, Massachusetts

This Summary of Abstracts contains all abstracts submitted for publication during calendar year 1978 by the staff and students of the Institution. Because some of the abstracts may not be published in the journal to which they have been submitted initially, we have purposely omitted identifying the journals . The volume is intended to be informative, but not a bibliography

Interactions between fisheries and birds in IJsselmeer, The Netherlands

IJsselmeer, a eutrophic, shallow lake (mean depth 4 m) of 180,000 ha, is heavily exploited by a fishery that catches dfl 11 million worth of eel Anguilla anguilla , perch Perca fluviatilis , pikeperch Stizostedion lucioperca and of the small zooplanktivorous smelt Osmerus eperlanus, the main prey for perch and pikeperch and for the piscivorous birds of IJsselmeer. The population of cormorant Phalacrocorax carbo affects the fisheries through its predation on perch and pikeperch, whereas black tern Chlidonias niger and black-headed gull Larus ridibundus are affected by the availability of smelt in IJsselmeer. The spatial distribution of prey fish and piscivorous birds was described as a function of spatial scale, water transparency and water depth. The carrying capacity of IJsselmeer for the production of prey fish was assessed, and a dynamic simulation model was constructed to predict consequences of fishery management measures on the fisheries and on the food availability for piscivorous birds.</p