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1.
BENJAMIN LEVY CHARLES COLLINS SUZANNE LENHART MARGUERITE MADDEN JOSEPH CORN RENÉ A. SALINAS WILLIAM STIVER 《Natural Resource Modeling》2016,29(1):71-97
Feral Hogs (Sus scrofa) are an invasive species that have occupied the Great Smoky Mountains National Park since the early 1900s. Recent studies on vegetation, mast, and harvest history were important for our work. Using these data, a model with discrete time and space was formulated to represent the feral hog dynamics in the Park. Management strategies and key characteristics of the population were investigated. The model uses observed mast variation to help govern population dynamics and results indicate that Park control efforts have limited the growth of the population. 相似文献
2.
A family of elliptic optimal control problems with pointwise constraints on control and state is considered. We are interested
in approximation of the optimal solution by a finite element discretization of the involved partial differential equations.
The discretization error for a problem with mixed state constraints is estimated in the semidiscrete case and in the fully
discrete scheme with the convergence of order h|ln h| and h
1/2, respectively. However, considering the unregularized continuous problem and the discrete regularized version, and choosing
suitable relation between the regularization parameter and the mesh size, i.e., ε∼h
2, a convergence order arbitrary close to 1, i.e., h
1−β
is obtained. Therefore, we benefit from tuning the involved parameters. 相似文献
3.
《Nonlinear Analysis: Hybrid Systems》2007,1(3):417-429
We consider the harvest of a certain proportion of a population that is modeled by an integrodifference equation, which is discrete in time and continuous in the space variable. The dispersal of the population is modeled by an integral of the growth function evaluated at the current population density against a kernel function. A concave growth function is used. In our model, growth occurs first, then dispersal and lastly harvesting control before the next generation. With the goal of maximizing the discounted profit stream, the optimal control is characterized by an optimality system. Illustrative examples are computed numerically. 相似文献
4.
Under geometric mixing condition, we presented asymptotic expansion of the distribution of an additive functional of a Markov
or an ε-Markov process with finite autoregression including Markov type semimartingales and time series models with discrete
time parameter. The emphasis is put on the use of the Malliavin calculus in place of the conditional type Cramér condition,
whose verification is in most case not easy for continuous time processes without such an infinite dimensional approach. In
the second part, by means of the perturbation method and the operational calculus, we proved the geometric mixing property
for non-symmetric diffusion processes, and presented a sufficient condition which is easily checked in practice. Accordingly, we
obtained asymptotic expansion of diffusion functionals and proved the validity of it under mild conditions, e.g., without
the strong contractivity condition.
Received: 7 September 1997 / Revised version: 17 March 1999 相似文献
5.
Matrix models of age-and/or stage-structured population dynamics rest upon the Perron-Frobenius theorem for nonnegative matrices,
and the life cycle graph for individuals of a given biological species plays a major role in model construction and analysis.
A summary of classical results in the theory of matrix models for population dynamics is presented, and generalizations are
proposed, which have been motivated by a need to account for an additional structure, i.e., to classify individuals not only
by age, but also by an additional (discrete) characteristic: size, physiological status, stage of development, etc.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 4, pp. 145–164, 2007. 相似文献
6.
In this article, we develop a numerical study of an optimal harvesting problem for age-dependent prey-predator system. Here, the rates of growth and decay as well as the interaction effect between species are assumed to be depending on age, time and space. Existence, uniqueness, and necessary conditions for the optimal control are assured in case of a small final time T. The discrete parabolic nonlinear dynamical systems are obtained by using a finite difference semi-implicit scheme. Then a numerical algorithm is developed to approximate the optimal harvesting effort and the optimal harvest. Results of the numerical tests are given. 相似文献
7.
J. L. Cieśliński 《Journal of Mathematical Sciences》2008,149(1):1032-1038
We present a large family of Spin(p, q)-valued discrete spectral problems. The associated discrete nets generated by the so-called Sym-Tafel formula are circular
nets (i.e., all elementary quadrilaterals are inscribed into circles). These nets are discrete analogues of smooth multidimensional
immersions in ℝm including isothermic surfaces, Guichard nets, and some other families of orthogonal nets.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 1, pp. 253–262, 2006. 相似文献
8.
Many recent advances in the theory of the optimal economic exploitation of renewable fish resources have been gained by applying optimal control theory. However, despite these successes, much less is known about how seasonal environments affect the maximum sustainable yield (MSY) (or population persistence) and any effects of relations between intensity and frequency of harvesting. Assuming that fish populations follow Beverton–Holt equations we investigated impulsive harvesting in seasonal environments, focusing on both economic aspects and resource sustainability. We first investigated the existence and stability of a periodic solution and its analytic formula, and then showed that the population persistence depends on the intensity and frequency of harvesting. With the MSY as a management objective, we investigated optimal impulsive harvesting policies. The optimal harvesting effort that maximizes the sustainable yield, the corresponding optimal population level, and the MSY are obtained by using discrete Euler–Lagrange equations and product formulae, and their explicit expressions were obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. These results imply that harvest timing is of crucial importance to the MSY. Since impulsive differential equations incorporate elements of continuous and discrete systems, we can apply all results obtained for Beverton–Holt equations with impulsive effects to periodic logistic equations with impulsive harvesting. 相似文献
9.
A fully discrete multi-level spectral Galerkin method in space–time for the two-dimensional nonstationary Navier–Stokes problem
is considered. The method is a multi-scale method in which the fully nonlinear Navier–Stokes problem is only solved on the
lowest-dimensional space
with the largest time step Δt
1; subsequent approximations are generated on a succession of higher-dimensional spaces
with small time step Δt
j by solving a linearized Navier–Stokes problem about the solution on the previous level. Some error estimates are also presented
for the J-level spectral Galerkin method. The scaling relations of the dimensional numbers and time mesh widths that lead to optimal
accuracy of the approximate solution in H
1-norm and L
2-norm are investigated, i.e., m
j∼m
j−1
3/2
, Δt
j∼Δt
j−1
3/2
, j=2,. . .,J. We demonstrate theoretically that a fully discrete J-level spectral Galerkin method is significantly more efficient than the standard one-level spectral Galerkin method.
Mathematics subject classifications (2000) 35L70, 65N30, 76D06
Subsidized by the Special Funds for Major State Basic Research Projects G1999032801-07, NSF of China 10371095 and the City
University of Hong Kong Research Project 7001093, NSF of China 50323001. 相似文献
10.
Chao Liu Qingling Zhang Xue Zhang Xiaodong Duan 《Journal of Computational and Applied Mathematics》2009,231(2):612-625
A differential-algebraic model system which considers a prey-predator system with stage structure for prey and harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, dynamic behavior of the proposed model system with and without discrete time delay is investigated. Local stability analysis of the model system without discrete time delay reveals that there is a phenomenon of singularity induced bifurcation due to variation of the economic interest of harvesting, and a state feedback controller is designed to stabilize the proposed model system at the interior equilibrium; Furthermore, local stability of the model system with discrete time delay is studied. It reveals that the discrete time delay has a destabilizing effect in the population dynamics, and a phenomenon of Hopf bifurcation occurs as the discrete time delay increases through a certain threshold. Finally, numerical simulations are carried out to show the consistency with theoretical analysis obtained in this paper. 相似文献
11.
Consider a discrete time queue with i.i.d. arrivals (see the generalisation below) and a single server with a buffer length
m. Let τm be the first time an overflow occurs. We obtain asymptotic rate of growth of moments and distributions of τm as m → ∞. We also show that under general conditions, the overflow epochs converge to a compound Poisson process. Furthermore,
we show that the results for the overflow epochs are qualitatively as well as quantitatively different from the excursion
process of an infinite buffer queue studied in continuous time in the literature. Asymptotic results for several other characteristics
of the loss process are also studied, e.g., exponential decay of the probability of no loss (for a fixed buffer length) in
time [0,η], η → ∞, total number of packets lost in [0, η, maximum run of loss states in [0, η]. We also study tails of stationary distributions. All results extend to the multiserver case and most to a Markov modulated
arrival process.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
12.
ABSTRACTIn portfolio optimization a classical problem is to trade with assets so as to maximize some kind of utility of the investor. In our paper this problem is investigated for assets whose prices depend on their past values in a non-Markovian way. Such models incorporate several features of real price processes better than Markov processes do. Our utility function is the widespread logarithmic utility, the formulation of the model is discrete in time. Despite the problem being a well-known one, there are few results where memory is treated systematically in a parametric model. Our algorithm is optimal and this optimality is guaranteed for a rich class of model specifications. Moreover, the algorithm runs online, i.e., the optimal investment is achieved in a day-by-day manner, using simple numerical integration, without Monte-Carlo simulations. Theoretical results are demonstrated by numerical experiments as well. 相似文献
13.
A. S. Makeev 《Computational Mathematics and Modeling》2007,18(1):1-9
Tikhonov’s regularization method is applied to numerical solution of inverse problems for two population models. For the first
model we solve the inverse problem that involves simultaneous determination of the mortality rate and the initial distribution
of individuals given supplementary information on population density. For the second model we determine the growth rate of
the individuals given additional information about their density. Examples of numerical solution are presented for both inverse
problems.
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Translated from Prikladnaya Matematika i Informatika, No. 23, pp. 5–14, 2006. 相似文献
14.
The net reproductive value n is defined for a general discrete linear population model with a non-negative projection matrix. This number is shown to have the biological interpretation of the expected number of offspring per individual over its life time. The main result relates n to the population's growth rate (i.e. the dominant eigenvalue λ of the projection matrix) and shows that the stability of the extinction state (the trivial equilibrium) can be determined by whether n is less than or greater than 1. Examples are given to show that explicit algebraic formulas for n are often derivable, and hence available for both numerical and parameter studies of stability, when no such formulas for λ are available. 相似文献
15.
I. G. Korepanov 《Journal of Mathematical Sciences》1999,94(4):1620-1629
A dynamical system in discrete time is studied by means of algebraic geometry. This system has reductions which can be interpreted
as classical field theory in the 2+1 discrete space-time. The study is based on the technique of vacuum curves and vacuum
vectors. The evolution of the system has hyperbolic character, i.e., has a finite propagation speed. Bibliography: 10 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 235, 1900, pp. 273–286. 相似文献
16.
This paper proposes easily-computed approximations to the finite-time expected waiting time for anM/G/1 system starting from an empty state. Both unsaturated (ρ<1) and saturated (ρ>1) conditions are considered. Numerical evidence is presented to indicate that the quality of the approximations is usefully
good, especially when ease of computation is an issue. Further, the methodology is adapted to assess expected waiting time
when inference must be made from a random sample of service times, and the decision is made to do so nonparametrically, i.e.,
without fitting a specific function. The results appear reasonable and potentially useful, and are not burdensome to obtain.
The methodology investigated can also be applied to the variety of queueing models that are close siblings ofM/G/1: priority and breakdowns and “vacations” being examples. Of course other approximating and inferential options remain to
be investigated. 相似文献
17.
A long-standing problem in forestry management is the optimal harvesting of a growing population of trees to maximize the resulting discounted aggregate net revenue. For an ongoing forest, the trees are harvested and replanted repeatedly; for a once-and-for-all forest, there is no replanting after a single harvest. In this paper, we outline a new formulation for the optimal-harvest problem which avoids difficulties associated with functional-differential equations or partial differential equations of state in the relevant optimal-control problem encountered in recent studies of the ongoing-forest problem. Our new formulation is based on the observation that tree logging is necessarily ordered by practical and/or regulatory considerations (e.g., it is illegal to cut the younger trees first in some jurisdictions); random access to tree sites does not occur in practice. The new formulation is described here for the simpler problem of a once-and-for-all forest. New results for nonuniform initial age distributions and variable unit harvest costs for this simpler problem are reported herein; results for an ongoing forest will be reported in [10]. The new model is also of interest from a control-theoretic viewpoint, as it exhibits the unique feature of having time as a state variable, in contrast to its usual role as an independent variable in conventional control problems. 相似文献
18.
We propose and analyze a fully discrete H
1-Galerkin method with quadrature for nonlinear parabolic advection–diffusion–reaction equations that requires only linear
algebraic solvers. Our scheme applied to the special case heat equation is a fully discrete quadrature version of the least-squares
method. We prove second order convergence in time and optimal H
1 convergence in space for the computer implementable method. The results of numerical computations demonstrate optimal order
convergence of scheme in H
k
for k = 0, 1, 2.
Support of the Australian Research Council is gratefully acknowledged. 相似文献
19.
《Nonlinear Analysis: Real World Applications》2003,4(4):639-651
In this paper, we established the exploitation of impulsive harvesting single autonomous population model by Logistic equation. By some special methods, we analysis the impulsive harvesting population equation and obtain existence, the explicit expression and global attractiveness of impulsive periodic solutions for constant yield harvest and proportional harvest. Then, we choose the maximum sustainable yield as management objective, and investigate the optimal impulsive harvesting policies respectively. The optimal harvest effort that maximizes the sustainable yield per unit time, the corresponding optimal population levels are determined. At last, we point out that the continuous harvesting policy is superior to the impulsive harvesting policy, however, the latter is more beneficial in realistic operation. 相似文献
20.
《Nonlinear Analysis: Theory, Methods & Applications》2007,66(12):2311-2341
Many recent advances in the theory of the optimal economic exploitation of renewable fish resources have been gained by applying optimal control theory. However, despite these successes, much less is known about how seasonal environments affect the maximum sustainable yield (MSY) (or population persistence) and any effects of relations between intensity and frequency of harvesting. Assuming that fish populations follow Beverton–Holt equations we investigated impulsive harvesting in seasonal environments, focusing on both economic aspects and resource sustainability. We first investigated the existence and stability of a periodic solution and its analytic formula, and then showed that the population persistence depends on the intensity and frequency of harvesting. With the MSY as a management objective, we investigated optimal impulsive harvesting policies. The optimal harvesting effort that maximizes the sustainable yield, the corresponding optimal population level, and the MSY are obtained by using discrete Euler–Lagrange equations and product formulae, and their explicit expressions were obtained in terms of the intrinsic growth rate, the carrying capacity, and the impulsive moments. These results imply that harvest timing is of crucial importance to the MSY. Since impulsive differential equations incorporate elements of continuous and discrete systems, we can apply all results obtained for Beverton–Holt equations with impulsive effects to periodic logistic equations with impulsive harvesting. 相似文献