Skip to main content

Abstract

Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Afifi L, El Jai A (1994) Strategic sensors and spy sensors. Int J Appl Math Comput Sci 4:553–573

    Google Scholar 

  • Afifi L, El Jai A (1995) Spy sensors and detection. Int J Syst Sci 26(3):1447–1463

    Google Scholar 

  • Afifi L, El Jai A (2015) Systèmes distribués perturbés. PUP, 342 pp

    Google Scholar 

  • Afifi L, El Jai A, Merry M (2000) Detection and sources reconstruction in a tube. Int J Syst Sci 31(2):149–159. PUP, Université de Perpignan, 346 pp

    Google Scholar 

  • Afifi L, Chafiai A, El Jai A (2001) Spatial compensation of boundary disturbances by boundary actuators. Int J Appl Math Comput Sci 11:9–20

    Google Scholar 

  • Afifi L, Chafiai A, El Jai A (2002) Regionally efficient and strategic actuators. Int J Syst Sci 33(1):1–12

    Article  Google Scholar 

  • Afifi L, Amimi N, Magri EM, El Jai A (2011) Regional domination in distributed systems. Int J Appl Math Sci 6(19):913–924

    Google Scholar 

  • Afifi L, El Jai A, Zerrik E (2012) Systems theory: regional analysis of infinite-dimensional linear systems. PUP, Perpignan, 425 pp

    Google Scholar 

  • Afifi L, Joundi M, Magri EM, El Jai A (2013a) Domination in controlled and observed distributed parameter systems. Intell Control Autom 4(2):217–226

    Article  Google Scholar 

  • Afifi L, Joundi M, Magri EM, El Jai A (2013b) An extended regional classification of distributed systems. Int J Math Anal 7(28):1363–1377

    Article  Google Scholar 

  • Afifi L, Joundi M, Amimi N, Bahadi M (2013c) Asymptotic classification of distributed linear systems. Appl Math Sci 7(51):2537–2554

    Google Scholar 

  • Aubin JP (1991) Viability theory. Birkhauser, Boston

    Google Scholar 

  • Aubin JP (2001) Viability kernels and capture basins of sets under differential inclusions. SIAM J Control Optim 40(3):853–881

    Article  Google Scholar 

  • Aubin J-P, Bayen AM, Saint-Pierre P (2011) Viability theory: new directions. Springer, Berlin. ISBN:978-3-642-16683-9

    Book  Google Scholar 

  • Bernoussi A (2007) Spreadability and vulnerability of distributed parameter systems. Int J Syst Sci 38(4):305–317

    Article  Google Scholar 

  • Bernoussi A (2010) Spreadability, vulnerability and protector control. Math Model Nat Phenom 5(07):145–150

    Article  Google Scholar 

  • Bernoussi A, Amharref M, Belfekih A (2015) Permanent protector control and viability for a class of distributed parameter systems. Accepted, to appear

    Google Scholar 

  • Curtain RF, Zwart HJ (1995) An introduction to infinite-dimensional linear systems theory. Texts in applied mathematics. Springer, New York

    Book  Google Scholar 

  • El Jai A (1991) Distributed systems analysis via sensors and actuators. Int J Sensors Actuators 29(1):1–11

    Article  Google Scholar 

  • El Jai A, Berrahmoune L (1984) Localisation d’actionneurs frontières pour la contrôlabilité de systèmes paraboliques, vol 298, Série I, N 8. Comptes rendus de l’Acadèmie des Sciences, Paris, pp 177–180

    Google Scholar 

  • El Jai A, Kassara K (1994) Spreadable distributed systems. Math Comput Model 20(1):47–64

    Article  Google Scholar 

  • El Jai A, Pritchard AJ (1988) Sensors and actuators in distributed systems analysis. Ellis Horwood series in applied mathematics, vol 47. Wiley, New York

    Google Scholar 

  • El Jai A, Simon MC, Zerrik E (1993) Regional observability and sensors structures. Int J Sensors Actuators 39(3):95–102

    Article  Google Scholar 

  • El Jai A, Pritchard AJ, Simon MC, Zerrik E (1995) Regional controllability of distributed systems. Int J Control 62:1351–1365

    Article  Google Scholar 

  • Gordon HS (1953) An economic approach to the optimum utilization of fishery resources. J Fish Res Bd Can 10:442447

    Article  Google Scholar 

  • Gordon HS (1954) The economics of a common property resource: the fishery. J Polit Econ 62:124142

    Article  Google Scholar 

  • Schaefer MB (1954) Some aspects of the dynamics of populations important to the management of commercial marine fisheries. Bull Inter-Amer Trop Tunna Comm 1:2756

    Google Scholar 

  • Smith VL (1969) On models of commercial fishing. J Polit Econ 77:181198

    Google Scholar 

  • Verhulst PF (1847) Notice sur la loi que la population suit dans son accroissement. Correspondance mathématique et physique de l’Observatoire de Bruxelles 10:113–121. https://play.google.com/store/books/details

    Google Scholar 

  • Verhulst PF (1847) Deuxième mémoire sur la loi d’accroissement de la population. Mémoires de l’Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique 20:1–32

    Google Scholar 

  • Zerrik E, El Jai A (2014) Stabilité des systèmes dynamiques. PUP, 302 pp

    Google Scholar 

  • Zerrik E, Badraoui L, El Jai A (1999) Sensors and regional boundary observability of parabolic systems. Int J Sensors Actuators 75:102–117

    Article  CAS  Google Scholar 

  • Zerrik E, Boutoulout A, El Jai A (2000) Actuators and regional boundary controllability for parabolic systems. Int J Syst Sci 31(1):73–82

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Abdelhaq El Jai or Marie Claude Simon El Jai .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Jai, A.E., Yacoubi, S.E., Jai, M.C.S.E., Mangeas, M., Douzal, V., Bernoussi, A.S. (2019). Mathematical Approach of Coviability: Concept, Modelling and Control. In: Barrière, O., et al. Coviability of Social and Ecological Systems: Reconnecting Mankind to the Biosphere in an Era of Global Change. Springer, Cham. https://doi.org/10.1007/978-3-319-78497-7_4

Download citation

Publish with us

Policies and ethics