A New Analytical Approach for Solving Van der Pol Oscillator
Md. Abul Kashem Mondal,
Md. Helal Uddin Molla,
Md. Shamsul Alam
Issue:
Volume 7, Issue 4, August 2019
Pages:
51-55
Received:
20 July 2019
Accepted:
16 September 2019
Published:
9 October 2019
Abstract: The Van der Pol oscillator is a nonlinear damping and non-conservative oscillator. Energy is generated at low amplitude and dissipated at high amplitude. This nonlinear oscillator was first introduced by Dutch electrical engineer and physicist B. Van der Pol and it was originally used to investigate vacuum tubes. Nowadays, it is used in both physical and biological sciences. It is also used in sociology and even in economics. It has a limit cycle and in earlier it was determined by the classical perturbation methods when the nonlinear term is small. Then the harmonic balance method was used to determine the limit cycle for stronger nonlinear case. Moreover, many researchers have been analyzed this oscillator by various numerical approaches. In this article, a new analytical approach based on harmonic balance method is presented to determine the limit cycle as well as approximate solutions of this nonlinear oscillator. The frequency as well as the limit cycle obtained by new approach has been compared with those obtained by other existing methods. The present method gives better result than other existing results and also close to the corresponding numerical result (considered to the exact result). Moreover, the present method is simpler than the existing harmonic balance method.
Abstract: The Van der Pol oscillator is a nonlinear damping and non-conservative oscillator. Energy is generated at low amplitude and dissipated at high amplitude. This nonlinear oscillator was first introduced by Dutch electrical engineer and physicist B. Van der Pol and it was originally used to investigate vacuum tubes. Nowadays, it is used in both physic...
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The Exchangeable Markov Multi-states Growth Process Incorporate with an Artificial Neural Network of Preterm Infants in an Incubator
Jean Pierre Namahoro,
Xiao Haijun
Issue:
Volume 7, Issue 4, August 2019
Pages:
56-62
Received:
6 August 2019
Accepted:
26 August 2019
Published:
9 October 2019
Abstract: The standard incubator used to monitor the development of preterm infants, with much attention for random optimization can interrupt the three main parameters (oxygen, environmental temperature, and humidity) responsible for preterm growth. The artificial neural network (ANN) has been recently proposed as a novel technique to control those parameters to provide a better and stabilized environment in an incubator. Unfortunately, this novel technique cannot continuously provide and indicate the update challenge of preterm growth. The objective of this paper is to apply a Markov multi-state growth process incorporates with multilayer feed-forward artificial neural network as an improved methodology to continuously control and provide an update of preterm growth in an incubator. The exchangeable Markov growth process, transition graph, and artificial neural network discussed on and applied in the designed incubator as methodology in paper and then make a joint density function of Markov multi-states growth process through multi-steps designed Algorithm to get the theoretical results. The updated measurements (weight, height, and head-perimeter) associated with controlled parameters used as input to the threshold logic unit (TLU) of ANN and then distinguish whether the growth process is abnormal or normal at each state. The summarized algorithm and multilayer feed-forward ANN utilized the panel data collected at Murunda hospital in Rwanda as input to show the application of improved methodology proposed in this paper, specifically, multi-state growth process of preterm infants across gender. As results, the continuous exchangeability of the growth process at each state has updated and may show abnormal or normal of growth process, and then sensors may notify these change through the joint density function of Markov multi-states growth process. Thus, improved methodology can increase the security and minimize time consumption in continuous monitoring growth process in an advanced way in time this idea has been implemented.
Abstract: The standard incubator used to monitor the development of preterm infants, with much attention for random optimization can interrupt the three main parameters (oxygen, environmental temperature, and humidity) responsible for preterm growth. The artificial neural network (ANN) has been recently proposed as a novel technique to control those paramete...
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