• Journal of the Korean Mathematical Society
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• v.61 no.3
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• pp.565-602
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• 2024

We study the collective behaviors of two second-order nonlinear consensus models with a bonding force, namely the Kuramoto model and the Cucker-Smale model with inter-particle bonding force. The proposed models contain feedback control terms which induce collision avoidance and emergent consensus dynamics in a suitable framework. Through the cooperative interplays between feedback controls, initial state configuration tends to an ordered configuration asymptotically under suitable frameworks which are formulated in terms of system parameters and initial configurations. For a two-particle system on the real line, we show that the relative state tends to the preassigned value asymptotically, and we also provide several numerical examples to analyze the possible nonlinear dynamics of the proposed models, and compare them with analytical results.

• Interdisciplinary Bio Central
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• v.2 no.4
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• pp.12.1-12.7
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• 2010

The National Bio Resource Project-Rat (NBRP-Rat) comprises the largest bank of laboratory rat (Rattus norvegicus) strains in the world. Its main focus is to develop infrastructure that will facilitate the systematic collection, preservation, and provision of rat strains. To breed effectively more than 180 rat strains in living stock, we establish the genetic control system in which a systematic set of genetic diagnoses and genetic monitoring are included. Genetic monitoring is performed by using 20 polymorphic markers. Monitoring is carried out when a living animal stock is re-established by using cryopreserved embryos or sperm or when a rat strain is first introduced to the NBRP-Rat by a depositor. Additional monitoring is then carried out on each strain every two years. Genetic diagnosis is performed largely by employing the Amp-FTA method. Protocols which detail how to perform a genetic diagnosis of 11 transgenes and 24 mutations have been made. Among the mutations, nine can be detected by simple gel electrophoresis of the PCR products, 11 by restriction enzyme treatment of the PCR products, and four by direct PCR product sequencing. Using this genetic control system, the NBRP-Rat can guarantee the genetic quality of its rat strains.