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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 15
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Articles

Qualitative analysis of a stock-effort parabolic model incorporating marine reserve

Pages 4045-4057 | Received 24 Jan 2022, Accepted 12 Jul 2022, Published online: 21 Jul 2022

References

  • Agardy MT. Advances in marine conservation: the role of marine protected areas. Trends Ecol Evol. 1994;9:267–270.
  • Allison GW, Lubchenco J, Carr MH. Marine reserves are necessary but not sufficient condition for marine conservation. Ecol Appl. 1994;8:79–92.
  • Anderson L. A bioeconomic analysis of marine reserves. Nat Resour Model. 2002;15:311–334.
  • Auger P, Moussaoui A, Sallet G. Basic reproduction ratio for a fishery model in a patchy environment. Acta Biotheor. 2012;60:167–188.
  • Du Y, Shi J. A diffusive predator–prey model with a protection zone. J Differ Equ. 2006;229:63–91.
  • Dugan JE, Davis GE. Applications of fishery refugia to coastal fishery management. Can J Fish Aquat Sci. 1993;50:2029–2042.
  • Luck T, Clark CW, Mangel M, et al. Implementing the precautionary principles in fisheries management through marine reserves. Ecol Appl. 1998;8:72–78.
  • Bensenane M, Moussaoui A, Auger P. On the optimal size of marine reserves. Acta Biotheor. 2013;61:109–118.
  • Moussaoui A, Auger P. Simple fishery and marine reserve models to study the SLOSS problem. ESAIM Proc Surv. 2015;49:78–90.
  • Cui R, Li H, Mei L, et al. Effect of harvesting quota and protection zone in a reaction–diffusion model arising from fishery management. Discrete Cont Dyn Syst B. 2017;22:791–807.
  • Auger P, Lett C, Moussaoui A, et al. Optimal number of sites in artificial pelagic multi-site fisheries. Can J Fish Aquat Sci. 2010;67:296–303.
  • Moussaoui A, Auger P P, Lett C. Optimal number of sites in multi-site fisheries with fish stock dependent migrations. Math Biosci Eng. 2011;8:769–783.
  • Crandall MG, Rabinowitz PH. Bifurcation from simple eigenvalues. J Funct Anal. 1971;8:321–340.
  • Amann H. Dynamics theory of quasilinear parabolic equation – I. Abstract evolution equation. Nonlinear Anal. 1997;12:219–250.
  • Sell GR, You Y. Dynamics of evolutionary equations, applied mathematical sciences, vol. 143. NY: Springer-Verlag; 2002.
  • Friedman A. Partial differential equations of parabolic type. Englewood Cliffs (NJ): Prentice-Hall, Inc.; 1964.
  • Henry D. Geometric theory of semilinear parabolic equations. Berlin: Springer; 1981. (Lecture notes in mathematics; vol. 840).
  • Pao CV. Nonlinear parabolic and elliptic equations. New York: Plenum; 1992.
  • Alikakos ND. An application of the invariance principle to reaction–diffusion equations. J Differ Equ. 1979;33:201–225.
  • Smith HL. Monotone dynamical systems. An introduction to the theory of competitive and cooperative systems, Math. Surveys Monogr., vol. 41. Providence (RI): American Mathematical Society; 1995.
  • Cantrell RS, Cosner C. On the dynamics of predator-prey models with the Beddington–DeAngelis functional response. J Math Anal Appl. 2001;257:206–222.
  • Cantrell RS, Cosner C. Spatial ecology via reaction–diffusion equations. Chichester: John Wiley-Sons, Ltd.; 2003. (Wiley series in mathematical and computational biology).
  • Smoller J. Shock waves and reaction diffusion equations. Berlin: Springer-Verlag; 1983.

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