Non‐linear structured population dynamics with co‐variates

References

• Artzrouni , M. 1986 . Une nouvelle famille de courbes de croissance: application à la transition démographique . Population , 3 : 497 – 510 .
   Google Scholar
• Aubin , J.‐P. 1997 . Dynamic Economic Theory: A Viability Approach. , Boston, Basel : Springer‐Verlag Birkhäuser .
   Google Scholar
• Aubin , J.‐P. 1991 . Viability Theory. , Boston, Basel : Birkhäuser .
   Google Scholar
• Aubin J.‐P. Bonneuil, N., Maurin, F. and Saint‐Pierre P. (submitted) Viability of pay‐as‐you‐go systems in an evolutionary environment.
   Google Scholar
• Aubin , J.‐P. and Frankowska , H. 1990 . Set‐Valued Analysis. , Boston : Basel . Birkhäuser
   Google Scholar
• Barbu, V. and Iannelli, M. (to appear). The semi‐group approach to nonlinear age‐structured equations.
   Google Scholar
• Barron , E. N. and Jensen , R. 1990 . Semicontinuous viscosity solutions for Hamilton‐Jacobi equations with convex Hamiltonians . Comm. Partial Differential Equations , 15 : 1713 – 1742 .
   Web of Science ®Google Scholar
• Bonneuil, N. (forthcoming). Viability in dynamic social networks. Journal of Mathematical Sociology.
   Google Scholar
• Bonneuil , N. 1998 . Population paths implied by the mean number of pairwise nucleotide differences among mitochondrial DNA sequences . Annals of Human Genetics , 62 : 61 – 73 .
   PubMedGoogle Scholar
• Bonneuil , N. 1998 . Games, equilibria, and population regulation under viability constraints: An interpretation of the work of the anthropologist Fredrik Barth . Population: An English selection , : 151 – 179 . special issue ‘New Methodological Approaches in Demography’
   Google Scholar
• Bonneuil , N. 1997 . Transformation of the French Demographic Landscape, 1806–1906. , Oxford : Oxford University Press .
   Google Scholar
• Bonneuil , N. 1997 . Introduction à la modélisation démographique. , Paris : Armand Colin, Collection U .
   Google Scholar
• Bonneuil , N. 1994a . Malthus, Boserup and population viability . Mathematical Population Studies , 4 (5) : 107 – 119 .
   Google Scholar
• Bonneuil , N. 1994b . Capital accumulation, inertia of consumption and norms of reproduction . Journal of Population Economics , 7 : 49 – 62 .
   PubMed Web of Science ®Google Scholar
• Bonneuil , N. and Müllers , K. 1997 . Viable populations in a prey‐predator system . Journal of Mathematical Biology , 35 : 261 – 293 .
   Google Scholar
• Bonneuil , N. and Saint‐Pierre , P. 2000 . Protected polymorphism in the two‐locus haploid model with unpredictable fitnesses . Journal of Mathematical Biology , 40 : 251 – 277 .
   PubMed Web of Science ®Google Scholar
• Bonneuil , N. and Saint‐Pierre , P. 1998 . Domaine de victoire et stratégies viables chez les pêcheurs décrits par l'anthropologue Fredrik Barth . Mathématiques, Informatique, et Sciences Humaines , 142 : 43 – 66 .
   Google Scholar
• Frankowska , H. 1993 . Lower semicontinuous solutions of Hamilton‐Jacobi‐Bellman equation . SIAM J. on Control and Optimization , 31 (1) : 257 – 272 .
   Web of Science ®Google Scholar
• Frankowska , H. 1989a . Optimal trajectories associated to a solution of contingent Hamilton‐Jacobi equations . Applied Mathematics and Optimization , 19 : 291 – 311 .
   Google Scholar
• Frankowska , H. 1989b . Hamilton‐Jacobi equation: viscosity solutions and generalized gradients . J. of Math. Analysis and Appl. , 141 : 21 – 26 .
   Web of Science ®Google Scholar
• Frankowska , H. and Quincampoix , M. 1991 . Viability kernels of differential inclusions with constraints: algorithm and applications . J. Math, of Systems, Estimation and Control , 1 (3) : 371 – 388 .
   Google Scholar
• Inaba , I. 1989 . Functional Analytic Approach to Age‐Structured Population Dynamics. , Rijksuniversiteit van Leiden . Ph.D. Thesis
   Google Scholar
• Iannelli , M. 1995 . Mathematical Theory of Age‐Structured Population Dynamics. , Pisa : Giardini .
   Google Scholar
• Keyfitz , N. 1985 . Applied Mathematical Demography. , New York, Berlin, Heidelberg : Springer Verlag .
   Google Scholar
• Keyfitz , N. 1968 . Introduction to the Mathematics of Population. , Reading, Massachussets : Addison‐Wesley .
   Google Scholar
• Keyfitz , B. and Keyfitz , N. 1997 . The McKendrick partial differential equation and its uses in epidmiology and population study . Math. Comput. Modelling , 26 : 1 – 9 .
   Google Scholar
• Ledermann , S. 1969 . Nouvelles tables‐types de mortalité , Paris : INED, PUF . Cahier 53
   Google Scholar
• Nagumo , M. 1942 . Über die Lage der integralkurven gewöhnlicher Differentialgleichungen . Proc. Phys. Math. Soc. Japan , 24 : 551 – 559 .
   Google Scholar
• Quincampoix , M. 1992 . Enveloppes d'invariance pour des inclusions différentielles Lipschitziennes: applications aux problèmes de cibles . Comptes‐Rendus de l'Académie des Sciences Paris , 314 : 343 – 347 .
   Google Scholar
• Saint‐Pierre , P. 1994 . Approximation of the viability kernel . Applied Math, and Optimisation , 29 : 187 – 209 .
   Web of Science ®Google Scholar
• Schoen , R. and Kim , Y. 1996 . Populations with quadratic exponential growth . Mathematical Population Studies , 6 (1) : 19 – 34 .
   Google Scholar
• Webb , G. 1985 . Theory of Nonlinear Age Dependent Population dynamics. , New York, Basel : Marcell Dekker .
   Google Scholar
• Corresponding author. E‐mail: [email protected]
   Google Scholar