Analysis of linear compartment models for ecosystems

Mulholland, Robert J.; Keener, Marvin S.

doi:10.1016/s0022-5193(74)80031-7

Cited by 46 publications

(15 citation statements)

References 11 publications

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“…Excellent introductions to the subject of compartmental dynamics can be found in the extensive literature (Atkins [1969], Jacquez [1972], Maeda et al [1978], Sandberg [1978]' Lewis and Anderson [1980a, b] and the literature cited therein). For the relevance of compartmental systems to ecological models, we refer to Mulholland and Keener [1974] and Mazanov [1976]. The dynamics of a simple n-compartment system is modelled by the autonomous system of ordinary differential equations where aOi is defined by (4.7.2).…”

Section: N([t])mentioning

confidence: 99%

Stability and Oscillations in Delay Differential Equations of Population Dynamics

Gopalsamy

1992

1,629

1,005

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Section: N([t])mentioning

confidence: 99%

Stability and Oscillations in Delay Differential Equations of Population Dynamics

Gopalsamy

1992

1,629

1,005

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“…If the system is actually linear, then neighborhood asymptotic stability ensures global stability (i.e., within all bounds of the system) (May 1974;Mulholland and Keener 1974). If the system is actually linear, then neighborhood asymptotic stability ensures global stability (i.e., within all bounds of the system) (May 1974;Mulholland and Keener 1974).…”

Section: Resultsmentioning

confidence: 99%

Nutrient Recycling and Stability: A Reevaluation

Harwell¹,

Cropper²,

Ragsdale³

1977

Ecology

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A general linear, donor controlled model of nutrient cycling in ecosystems has been previously developed. Stability analysis of this model was equated to analysis of the parameters of the second-order damped oscillation equation, and rankings among eight aquatic and terrestrial ecosystems were ascertained by those authors. In this paper, the results of direct experimental perturbations of the general model and the second-order approximation are presented. These digital and analog computer analyses show that the terms said by those authors to measure the resistance and resilience components of asymptotic stability do not reflect the actual response of either stability component for either model. Ecosystem resilience and resistance rankings, based upon the linear models, are reassigned according to observed temporal response.

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“…, (4,41) By applying Theorem 4, 2 it follows from the above that for q(t) = q(t + T) there exists a unique T-periodic solution to the co-state system to which all other solutions converge, The optimal control for the linear periodic control problem is given by , (4,42) The matrices R(t) and B(t) will in general be T-periodic as previously …”

Section: Periodic Solutions To the Linear Periodic Control Problemmentioning

confidence: 99%

“…Keener [42] showing the existence of positive solutions to the state equations for the linear donor control compartment model. The proof rests on the diagonal dominance of the coefficient matrix as described in Equation (4,5).…”

Section: The Linear Periodic Control Problemmentioning

confidence: 99%