An application of traveling wave analysis in economic growth model

Zhou, Ming-Chun; Yang, Yanfang

doi:10.1016/j.amc.2007.11.006

Cited by 3 publications

(4 citation statements)

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“…Fisher's assumptions for a sexually reproducing species lead to a Huxley reaction-diffusion equation, with cubic logistic source term for the gene frequency of a mutant advantageous recessive gene [9]. Fisher's equation more accurately represents the spread of an advantaged mutant strain within an asexual species [10].…”

Section: Biological Engineeringmentioning

confidence: 99%

“…Today wavelet is not only the workspace in computer imaging and animation; they are also used by the FBI to encode its data base of million fingerprints. In future, scientist may put wavelet analysis for diagnosing breast cancer, looking for heart abnormalities, predicting the weather, signal processing, data compression, smoothing and image compression [9], fingerprints verification, DNA analysis, protein analysis, Blood-pressure, heart-rate and ECG analysis, finance, internet traffic description, speech recognition and computer graphics.…”

Section: Wavelet Analysismentioning

confidence: 99%

“…The wavelet transform has been perhaps the most exciting development in the decade to bring together researchers in several different field such as signal processing, quantum mechanics, image processing [37,9], communications, computer science and mathematics -to name a few as in [40]. Today wavelet is not only the workspace in computer imaging and animation; they are also used by the FBI to encode its data base of million fingerprints.…”

Section: Wavelet Analysismentioning

confidence: 99%

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Review of wavelet methods for the solution of reaction–diffusion problems in science and engineering

Hariharan

Kannan

2014

Applied Mathematical Modelling

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a b s t r a c tWavelet method is a recently developed tool in applied mathematics. Investigation of various wavelet methods, for its capability of analyzing various dynamic phenomena through waves gained more and more attention in engineering research. Starting from 'offering good solution to differential equations' to capturing the nonlinearity in the data distribution, wavelets are used as appropriate tools at various places to provide good mathematical model for scientific phenomena, which are usually modeled through linear or nonlinear differential equations. Review shows that the wavelet method is efficient and powerful in solving wide class of linear and nonlinear reaction-diffusion equations. This review intends to provide the great utility of wavelets to science and engineering problems which owes its origin to 1919. Also, future scope and directions involved in developing wavelet algorithm for solving reaction-diffusion equations are addressed.Crown

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Section: Biological Engineeringmentioning

confidence: 99%

Section: Wavelet Analysismentioning

confidence: 99%

Section: Wavelet Analysismentioning

confidence: 99%

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Review of wavelet methods for the solution of reaction–diffusion problems in science and engineering

Hariharan

Kannan

2014

Applied Mathematical Modelling

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“…The first case is studied for example in Quah [37], Camacho et al [15], Boucekkine et al [8], Brito [10,11], Zhou [40]. This modeling reflects the mobility of capital or individuals, and implies a physical diffusion of human or physical capital.…”

Section: Introductionmentioning

confidence: 99%

Spatial externality and indeterminacy

Augeraud-Véron

Ducrot

2019

Math. Model. Nat. Phenom.

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We study conditions for existence and uniqueness of solutions in some space-structured economic models with long-distance interactions between locations. The solution of these models satisfies non local equations, in which the interactions are modeled by convolution terms. Using properties of the spectrum location obtained by studying the characteristic equation, we derive conditions for the existence and uniqueness of the solution. This enables us to characterize the degree of indeterminacy of the system being considered. We apply our methodology to a theoretical one-sector growth model with increasing returns, which takes into account technological interdependencies among countries that are modeled by spatial externalities. When symmetric interaction kernels are considered, we prove that conditions for which indeterminacy occurs are the same as the ones needed when no interactions are taken into account. For Gaussian kernels, we study the impact of the standard deviation parameter on the degree of indeterminacy. We prove that when some asymmetric kernels are considered, indeterminacy can occur with classical assumptions on supply and demand curves.

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