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  • 1
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 438 (2005), S. 355-359 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Population-level analyses often use average quantities to describe heterogeneous systems, particularly when variation does not arise from identifiable groups. A prominent example, central to our current understanding of epidemic spread, is the basic reproductive number, R0, which is ...
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  • 2
    Publication Date: 2013-08-31
    Description: So-called differential games of kind (qualitative games) were considered involving two or more players each of whom possesses a target toward which he wished to steer the response of a dynamical system that was under the control of all players. Sufficient conditions were derived, which assure termination on a particular player's target. In general, these conditions were constructive in that they permited construction of a winning (terminating) strategy for a player. The theory is illustrated by a pursuit-evasion problem.
    Keywords: SYSTEMS ANALYSIS
    Type: NASA-CR-152044
    Format: application/pdf
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  • 3
    ISSN: 1432-1416
    Keywords: Stability ; Discrete population models ; Bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Sufficiency conditions for local stability are derived for a class of density dependent Leslie matrix models. Four of the recruitment functions in common use in fisheries management are then considered. In two of these oscillating instability can never occur (Beverton and Holt and Cushing forms). In the other two (Deriso-Schnute and Shepherd forms) undamped oscillations are possible within the region of parameter space described here. An algorithm is developed for calculating necessary and sufficient local stability conditions for a simplified form of the general age-structured model. The complete spectrum of stability states (monotonic stability; monotonic instability; oscillating-stable; oscillating-unstable) and the bifurcation periods are given for selected examples of this model. The examples cover a large portion of the parameter space of interest in resource management. It is shown that in perfectly deterministic systems which are observed with error, oscillating instabilities may be missed, and such systems could be erroneously assumed to be stable.
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  • 4
    ISSN: 1432-1351
    Keywords: Honeybee ; Olfaction ; Synergism ; Inhibition ; Concentration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Abstract Recordings were made from single sensilla placodea of the worker honeybee (Apis mellifera). The sensilla were stimulated with one of two sets of four compounds and their binary mixtures, at two dosage levels. Aromatic compounds comprised one set, and saturated n-octane derivatives comprised the other set. Correlation, principal component, and cluster analyses indicate that responses to binary mixtures are not linear combinations of responses to the component compounds. The first principal component indicated that neuronal units had either more excitatory or more inhibitory responses to all odorants than would be expected from a model where inhibitory and excitatory responses are randomly distributed among the neuronal units. When compared to the responses to the component odorants, synergistic responses to binary odors occurred more often than would be expected by chance. Clear inhibitory responses to binary odors were less prevalent. This study agrees with an earlier study employing aromatic odorants in that most of the aromatic odorants each had groups of receptor neurons that were relatively selective for it, and each odorant had a distinctly different number of receptor neurons selective for it. Among the octane derivatives, receptor neurons were selective for the level of oxidation of the functional group or its site of attachment, rather than specific compounds.
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  • 5
    ISSN: 1573-2878
    Keywords: State-variable discontinuities ; maximum principle ; fisheries management ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Consideration is given to continuous-time, parameter-dependent optimal control problems with state-variable jump discontinuities atN variable interior times. A maximum principle involving known costate jump conditions is stated and is proved by transforming the problem into a standard Mayer control problem. An illustrative example for fisheries management is included.
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  • 6
    ISSN: 1573-2878
    Keywords: Pest management ; feedback control ; optimal application of pesticides
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A class of distributed-parameter optimal control problems whose system dynamics are more akin to those of systems of ordinary differential equations is presented together with a set of necessary conditions for optimality. It is shown that certain insect pest management problems fall within the ambit of this theory, which is then used to investigate the properties of the optimal pesticide application schedule and to synthesize a part-feedback control strategy. This latter strategy is presented in a way which makes it applicable to devising strategies for the application of pesticides in agricultural systems that are too complex to be easily modeled, but for which correlations are available between pest levels at certain points during the growing season and yield losses.
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  • 7
    ISSN: 1573-2878
    Keywords: Resource management ; optimal harvesting ; maximum sustainable yield
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A natural extension of age structured Leslie matrix models is to replace age classes with stage classes and to assume that, in each time period, the transition from one stage class to the next is incomplete; that is, diagonal terms appear in the transition matrix. This approach is particularly useful in resource systems where size is more easily measured than age. In this linear setting, the properties of the models are known; and these models have been applied to the analysis of population problems. A more applicable setting is to assume that the reproduction, survival, and transition parameters in the model are density dependent. The behavior of such models is determined by the form of this density dependence. Here, we focus on models in which the parameters depend on the value of an aggregated variable, defined to be the weighted sum of the number of individuals in each stage class. In forestry models, for example, this aggregated variable may represent a basal area index; in fisheries models, it may represent a spawning stock biomass. Current age structured nonlinear stock-recruitment fisheries models are a special case of the models considered here. Certain results that apply to age structured models can be extended to this broader class of models. In particular, the questions addressed relate to the minimum number of age classes that need to be harvested to obtain maximum sustainable yield policies and to managing resources under nonequilibrium and stochastic conditions. Application of the model to problems in fisheries, forestry, pest, and wildlife management is also discussed.
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  • 8
    ISSN: 1573-2878
    Keywords: Optimal harvesting ; age-structured models ; cohort analysis ; sustainable yields ; feedback control ; fisheries management
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A Beverton and Holt type linear cohort dynamics model is integrated and combined with a nonlinear stock-recruitment relationship to obtain a discrete-time multicohort harvesting model. Assuming that each age class is individually controllable, it is shown, subject to certain assumptions, that the optimal harvesting strategy is to drive the population to the maximum sustainable yield solution in one time step. In most fisheries, this controllability assumption is not met and harvesting is agewise nonselective. In this case, it may be preferable to implement a harvesting policy based on suboptimal constant effort or stock level feedback strategies, rather than implement a more complicated optimal policy. This question is addressed through numerical studies on the management of an anchovy fishery.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1573-2878
    Keywords: Population harvesting ; competing populations ; singular control ; renewable resource management ; resource management
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of harvesting two competing populations is formulated in an optimal control setting. The maximum sustained rent (MSR) solution is introduced and is shown to be not only totally singular, but also to play a central role in solutions to the harvesting problem. It is further shown that nonsingular extremal subarcs must in general approach and leave the MSR along partially singular curves. A numerical example is introduced to demonstrate this phenomenon. In the case where the populations are driven onto the MSR in minimum time, however, the optimal control is shown to be bang-bang with at most one switch.
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  • 10
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit-evasion ; homicidal chauffeur ; Lyapunov methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two-target versions of the game of two cars and the homicidal chauffeur game are introduced. This enables us to consider pursuitevasion withouta priori role assignment. A generic example of the two-target homicidal chauffeur game is considered in detail; in particular, a map of the game and its corresponding winning strategies are found using Lyapunov methods of analysis. The effects of altering game parameters, such as the speed and maneuverability ratios, and the weapon system parameters are then presented. It is found that certain winning strategies include a swerve-type maneuver and that, for certain sets of parameters, regions of stagnation and different modes of draw occur.
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