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Journal of Modern Mathematics Frontier    Follow    
  This is an Open Access Journal Open Access journal
     ISSN (Print) 2227-3743 - ISSN (Online) 2227-3751
     Published by Science and Engineering Publishing Company Homepage  [46 journals]
  • Multiperiodicity of High-Order BAM Networks on Time Scales
    • Abstract: Multiperiodicity of High-Order BAM Networks on Time Scales
      Pages 125-128
      Author Honghua BinZhenkun HuangJinxiang Ca
      This brief paper presents new results about dynamics of high-order bidirectional associative memory (BAM) networks on time scales. Invariant sets on time scales are constructed to orientate regions of orbits. By partitions of index sets, we obtain a unique (periodic) trajectory which is exponentially attractive in each invariant set.
      PubDate: 2013-12
  • Solving Partial Differential Equations with Chaotic Asynchronous Schemes
           in Multi-Interaction Systems
    • Abstract: Solving Partial Differential Equations with Chaotic Asynchronous Schemes in Multi-Interaction Systems
      Pages 129-140
      Author Pascal RedouZakaria BelemaalemMarc Parenthoe
      Within the framework of multi-interaction systems (MIS), we aim at proposing algorithms for solving some partial differential equations (PDE), that are commonly used for modeling phenomena like transport or diffusion, as they often occur in a complex system involving natural phenomena. Unlike classical synchronous ones, schemes for MIS have to be compatible with chaotic asynchronous iterations, which enable multi-model/scale, interactive and real-time simulations. In our context, the notion of asynchronous iteration expresses the fact that activities, each modeling a phenomenon, have their own lifetime and are processed one after the other. These activations are processed by cycles, in a random order -to avoid computation bias-, what we name chaotic iterations. We provide MIS-compatible schemes to simulate transport phenomena, thermal diffusion phenomena and the spreading phenomenon of a wave packet. Our schemes are based on interactions that represent sorts of Maxwell daemons: transfers of flows between several separate environments given by a spatial resolution grid. We establish formal proofs of convergence for our transport methods. We experiment an efficient asynchronous diffusion scheme, and couple both schemes for solving the advection-diffusion problem. We finally illustrate a multi-interaction method for the spreading of a wave packet described by the Schrödinger equation. Results are compared to classical numerical methods and they show that our methods are as accurate as classical ones, whilst respecting MIS constraints.
      PubDate: 2013-12
  • On Association Coefficients, Correction for Chance, and Correction for
           Maximum Value
    • Abstract: On Association Coefficients, Correction for Chance, and Correction for Maximum Value
      Pages 111-119
      Author Matthijs J. Warren
      This paper studied correction for chance and correction for maximum value as functions on a space of association coefficients. Various properties of both functions are presented. It is shown that the two functions commute under composition; and that the composed function maps a coefficient and all its linear transformations given the marginal totals to the same coefficient. The results presented in the paper have generalized various results from the literature.
      PubDate: 2013-12
  • Robust Synchronization of Fractional-order PMSM Chaotic System
    • Abstract: Robust Synchronization of Fractional-order PMSM Chaotic System
      Pages 120-124
      Author Dongfeng WangJinying ZhangShitong YuanYanyan Re
      Permanent magnet synchronous motor (PMSM) shows bifurcation and chaotic behavior under parameters perturbation. In this paper, based on linear matrix inequalities (LMI), a synchronization controller was designed in allusion to the fractional-order PMSM mathematical model. It has been proved that the fractional-order chaotic system can achieve robust synchronization with appropriate controller parameters under any initial value and parameters perturbation. The numerical simulation results of fractional-order PMSM chaotic system validated the efficiency of the proposed robust controller.
      PubDate: 2013-12
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