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  • Mathematics  (14)
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  • Mathematics  (14)
  • 1
    Online Resource
    Online Resource
    Optimal Control of Polymer Flooding Based on Maximum Principle
    Hindawi Limited ; 2012
    In:  Journal of Applied Mathematics Vol. 2012 ( 2012), p. 1-20
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2012 ( 2012), p. 1-20
    Abstract: Polymer flooding is one of the most important technologies for enhanced oil recovery (EOR). In this paper, an optimal control model of distributed parameter systems (DPSs) for polymer injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding, and the inequality constraint as the polymer concentration limitation. To cope with the optimal control problem (OCP) of this DPS, the necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagin’s weak maximum principle. A gradient method is proposed for the computation of optimal injection strategies. The numerical results of an example illustrate the effectiveness of the proposed method.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2012/987975
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2012
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 2
    Online Resource
    Online Resource
    A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-7
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-7
    Abstract: Anderson's inequality (Anderson, 1958) as well as its improved version given by Fink (2003) is known to provide interesting examples of integral inequalities. In this paper, we establish local fractional integral analogue of Anderson's inequality on fractal space under some suitable conditions. Moreover, we also show that the local fractional integral inequality on fractal space, which we have proved in this paper, is a new generalization of the classical Anderson's inequality.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/797561
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 3
    Online Resource
    Online Resource
    Analysis of a Patch Model for the Dynamical Transmission of Echinococcosis
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-13
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-13
    Abstract: A patch model for echinococcosis due to dogs migration is proposed to explore the effect of dogs migration among patches on the spread of echinococcosis. We firstly define the basic reproduction number R 0 . The mathematical results show that the dynamics of the model can be completely determined by R 0 . If R 0 〈 1 , the disease-free equilibrium is globally asymptotically stable. When R 0 〉 1 , the model is permanence and endemic equilibrium is globally asymptotically stable. According to the simulations, it is shown that the larger diffusion of dogs from the lower epidemic areas to the higher prevalence areas can intensify the spread of echinococcosis. However, the larger diffusion of dogs from the higher prevalence areas to the lower epidemic areas can reduce the spread and is beneficial for disease control.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/576365
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 4
    Online Resource
    Online Resource
    Global Behaviors of a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-18
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-18
    Abstract: We study a class of discrete SIRS epidemic models with nonlinear incidence rate F ( S ) G ( I ) and disease-induced mortality. By using analytic techniques and constructing discrete Lyapunov functions, the global stability of disease-free equilibrium and endemic equilibrium is obtained. That is, if basic reproduction number ℛ 0 〈 1 , then the disease-free equilibrium is globally asymptotically stable, and if ℛ 0 〉 1 , then the model has a unique endemic equilibrium and when some additional conditions hold the endemic equilibrium also is globally asymptotically stable. By using the theory of persistence in dynamical systems, we further obtain that only when ℛ 0 〉 1 , the disease in the model is permanent. Some special cases of F ( S ) G ( I ) are discussed. Particularly, when F ( S ) G ( I ) = β S I / ( 1 + λ I ) , it is obtained that the endemic equilibrium is globally asymptotically stable if and only if ℛ 0 〉 1 . Furthermore, the numerical simulations show that for general incidence rate F ( S ) G ( I ) the endemic equilibrium may be globally asymptotically stable only as ℛ 0 〉 1 .
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/249623
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 5
    Online Resource
    Online Resource
    Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-9
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-9
    Abstract: Predator-prey models describe biological phenomena of pursuit-evasion interaction. And this interaction exists widely in the world for the necessary energy supplement of species. In this paper, we have investigated a ratio-dependent spatially extended food chain model. Based on the bifurcation analysis (Hopf and Turing), we give the spatial pattern formation via numerical simulation, that is, the evolution process of the system near the coexistence equilibrium point ( u 2 * , v 2 * , w 2 * ) , and find that the model dynamics exhibits complex pattern replication. For fixed parameters, on increasing the control parameter c 1 , the sequence “holes → holes-stripe mixtures → stripes → spots-stripe mixtures → spots” pattern is observed. And in the case of pure Hopf instability, the model exhibits chaotic wave pattern replication. Furthermore, we consider the pattern formation in the case of which the top predator is extinct, that is, the evolution process of the system near the equilibrium point ( u 1 * , v 1 * , 0 ) , and find that the model dynamics exhibits stripes-spots pattern replication. Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/130851
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 6
    Online Resource
    Online Resource
    Exact Finite Difference Scheme and Nonstandard Finite Difference Scheme for Burgers and Burgers-Fisher Equations
    Hindawi Limited ; 2014
    In:  Journal of Applied Mathematics Vol. 2014 ( 2014), p. 1-12
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2014 ( 2014), p. 1-12
    Abstract: We present finite difference schemes for Burgers equation and Burgers-Fisher equation. A new version of exact finite difference scheme for Burgers equation and Burgers-Fisher equation is proposed using the solitary wave solution. Then nonstandard finite difference schemes are constructed to solve two equations. Numerical experiments are presented to verify the accuracy and efficiency of such NSFD schemes.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2014/597926
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 7
    Online Resource
    Online Resource
    Left and Right Inverse Eigenpairs Problem for κ -Hermitian Matrices
    Hindawi Limited ; 2013
    In:  Journal of Applied Mathematics Vol. 2013 ( 2013), p. 1-6
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2013 ( 2013), p. 1-6
    Abstract: Left and right inverse eigenpairs problem for κ -hermitian matrices and its optimal approximate problem are considered. Based on the special properties of κ -hermitian matrices, the equivalent problem is obtained. Combining a new inner product of matrices, the necessary and sufficient conditions for the solvability of the problem and its general solutions are derived. Furthermore, the optimal approximate solution and a calculation procedure to obtain the optimal approximate solution are provided.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2013/230408
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2013
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 8
    Online Resource
    Online Resource
    Infinitely Many Periodic Solutions for Nonautonomous Sublinear Second-Order Hamiltonian Systems
    Hindawi Limited ; 2010
    In:  Abstract and Applied Analysis Vol. 2010 ( 2010), p. 1-10
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2010 ( 2010), p. 1-10
    Abstract: Two sequences of distinct periodic solutions for second-order Hamiltonian systems with sublinear nonlinearity are obtained by using the minimax methods. One sequence of solutions is local minimum points of functional, and the other is minimax type critical points of functional. We do not assume any symmetry condition on nonlinearity.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2010/620438
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2010
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 9
    Online Resource
    Online Resource
    Spatial Complexity of a Predator-Prey Model with Holling-Type Response
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-15
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-15
    Abstract: We focus on a spatially extended Holling-type IV predator-prey model that contains some important factors, such as noise (random fluctuations), external periodic forcing, and diffusion processes. By a brief stability and bifurcation analysis, we arrive at the Hopf and Turing bifurcation surface and derive the symbolic conditions for Hopf and Turing bifurcation on the spatial domain. Based on the stability and bifurcation analysis, we obtain spiral pattern formation via numerical simulation. Additionally, we study the model with a color noise and external periodic forcing. From the numerical results, we know that noise or external periodic forcing can induce instability and enhance the oscillation of the species density, and the cooperation between noise and external periodic forces inherent to the deterministic dynamics of periodically driven models gives rise to the appearance of a rich transport phenomenology. Our results show that modeling by reaction-diffusion equations is an appropriate tool for investigating fundamental mechanisms of complex spatiotemporal dynamics.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/675378
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 10
    Online Resource
    Online Resource
    Recent Developments on Time-Delay Neural Networks
    Hindawi Limited ; 2015
    In:  Abstract and Applied Analysis Vol. 2015 ( 2015), p. 1-1
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2015 ( 2015), p. 1-1
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2015/865409
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2015
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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