On the growth of a population dependent on ages and involving resources and pollution

Haimovici, Adolf

doi:10.1016/0025-5564(79)90050-6

Cited by 15 publications

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“…P 2 (0, t) = j fc 2 (a, P 1 (t-i), P 2 (t))p 2 (a, t)da , [7] and Rotenberg [S]). The question of the relation between an age independent system and a corresponding age dependent system has been considered by Gurtin and MacCamy [4] and Gurtin and Levine [6] who have established an asymptotic (as t •*• °° ) relation between such models by constructing a higher dimensional lumped parameter system (in terms of ordinary differential equations) to represent the age dependent distributed parameter system.…”

Section: P (0 T) = \ B [A Pat) Pat-t))paa T)da mentioning

confidence: 99%

“…The question of the relation between an age independent system and a corresponding age dependent system has been considered by Gurtin and MacCamy [4] and Gurtin and Levine [6] who have established an asymptotic (as t •*• °° ) relation between such models by constructing a higher dimensional lumped parameter system (in terms of ordinary differential equations) to represent the age dependent distributed parameter system. Assuming the existence of stationary age distributions Haimovici [7] considers their stability in a system of two interacting populations explicitly taking into consideration the dynamical nature of the habitat's resources and pollution.…”

Section: P (0 T) = \ B [A Pat) Pat-t))paa T)da mentioning

confidence: 99%

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Time lags and density dependence in age dependent two species competition

Gopalsamy

1982

Bull. Austral. Math. Soc.

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Sufficient conditions are obtained for the existence and linear stability of time independent age distributions in two species competition with age and time lagged density dependent mortality and fertility functions. Let P.(t) and P^[t) denote the total population sizes (or biomasses) at time t 5 0 of two interacting species living in a common habitat and competing for a common pool of resources. The competition for resources will be implicit in our model similar to that in the two species Lotka-Volterra competition system. Assuming constant sex ratios in the two species we can consider P (fc) and PAt) Introductionto be the population of females only; immigration, emigration and internal dispersion in the habitat are assumed to play no significant role in the dynamics of the community.We suppose that the two species contain respectively P, (a, t)da and pAa, t)da individuals with ages between a and a + da (a > 0) at time t so that we haveReceived 13 October 198l. .available at https://www.cambridge.org/core/terms. https://doi

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Section: P (0 T) = \ B [A Pat) Pat-t))paa T)da mentioning

confidence: 99%

Section: P (0 T) = \ B [A Pat) Pat-t))paa T)da mentioning

confidence: 99%

Time lags and density dependence in age dependent two species competition

Gopalsamy

1982

Bull. Austral. Math. Soc.

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“…Such a direct interaction variable could determine the amount of occupied territory or a quasi steady state approximation of food concentration under the assumption that food consumption is much faster than the demographic processes of birth and death. Haimovici (1979) and Gyllenberg (1982) treated age-structured models with indirect interaction variables, which satisfy differential equations with the right hand sides involving the age-distribution, hence taking the form of integro-differential equations. Gyllenberg (1983) proved the stability part of the principle of linearized stability for a model containing both direct and indirect interaction variables.…”

Section: Physiologically Structured Populations and Interaction Via Tmentioning

confidence: 99%