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Suppressive Influence of Time- Space White Noise on the Explosion of Solutions of Stochastic Fokker- Planck Delay Differential Equations
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作者 Augustine O. Atonuje Jonathan Tsetimi 《Journal of Mathematics and System Science》 2016年第7期284-290,共7页
It is generally known that the solutions of deterministic and stochastic differential equations (SDEs) usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventual... It is generally known that the solutions of deterministic and stochastic differential equations (SDEs) usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion. 展开更多
关键词 Explosion non-linear stochastic Fokker Planck delay differential equation time - space white noise finite time.
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An Effective Density Based Approach to Detect Complex Data Clusters Using Notion of Neighborhood Difference 被引量:4
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作者 S. Nagaraju Manish Kashyap Mahua Bhattachraya 《International Journal of Automation and computing》 EI CSCD 2017年第1期57-67,共11页
The density based notion for clustering approach is used widely due to its easy implementation and ability to detect arbitrary shaped clusters in the presence of noisy data points without requiring prior knowledge of ... The density based notion for clustering approach is used widely due to its easy implementation and ability to detect arbitrary shaped clusters in the presence of noisy data points without requiring prior knowledge of the number of clusters to be identified. Density-based spatial clustering of applications with noise (DBSCAN) is the first algorithm proposed in the literature that uses density based notion for cluster detection. Since most of the real data set, today contains feature space of adjacent nested clusters, clearly DBSCAN is not suitable to detect variable adjacent density clusters due to the use of global density parameter neighborhood radius Y,.ad and minimum number of points in neighborhood Np~,. So the efficiency of DBSCAN depends on these initial parameter settings, for DBSCAN to work properly, the neighborhood radius must be less than the distance between two clusters otherwise algorithm merges two clusters and detects them as a single cluster. Through this paper: 1) We have proposed improved version of DBSCAN algorithm to detect clusters of varying density adjacent clusters by using the concept of neighborhood difference and using the notion of density based approach without introducing much additional computational complexity to original DBSCAN algorithm. 2) We validated our experimental results using one of our authors recently proposed space density indexing (SDI) internal cluster measure to demonstrate the quality of proposed clustering method. Also our experimental results suggested that proposed method is effective in detecting variable density adjacent nested clusters. 展开更多
关键词 Density based clustering neighborhood difference density-based spatial clustering of applications with noise (DBSCAN) space density indexing (SDI) core object.
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New Exact Solutions for the Wick-Type Stochastic Kudryashov–Sinelshchikov Equation
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作者 S.Saha Ray S.Singh 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第2期197-206,共10页
In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stoch... In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stochastic Kudryashov–Sinelshchikov equation to deterministic partial differential equation. Also we have applied inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space. 展开更多
关键词 Kudryashov–Sinelshchikov Wick-product White noise space improved Sub-equation method Hermite transform inverse Hermite transform
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