Novel Approach for a van der Pol Oscillator in the Continuous Time Domain
作者： Junaid Ali Khan , Muhammad Asif Zahoor Raja , Ijaz Mansoor Qureshi
DOI: 10.1088/0256-307X/28/11/110205
关键词: Statistical analyses 、 Reliability (statistics) 、 Van der Pol oscillator 、 Algorithm 、 Computer science 、 Simulated annealing 、 Artificial neural network 、 Time domain
摘要: We investigate the continuous time domain numerical treatment of a van der Pol oscillator, applying trial solution as an artificial feed-forward neural network model containing unknown adjustable parameters. The optimization is performed by simulated annealing in unsupervised method. proposed scheme tested successfully its application both non-stiff and stiff conditions. Its reliability effectiveness validated through comprehensive statistical analyses. obtained results are good agreement with classical RK45
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Ken-Ichi Funahashi, On the approximate realization of continuous mappings by neural networks Neural Networks. ,vol. 2, pp. 183- 192 ,(1989) , 10.1016/0893-6080(89)90003-8
MAKOTO ITOH, SYNTHESIS OF ELECTRONIC CIRCUITS FOR SIMULATING NONLINEAR DYNAMICS International Journal of Bifurcation and Chaos. ,vol. 11, pp. 605- 653 ,(2001) , 10.1142/S0218127401002341
D.W. Storti, R.H. Rand, Dynamics of two strongly coupled van der pol oscillators International Journal of Non-Linear Mechanics. ,vol. 17, pp. 143- 152 ,(1982) , 10.1016/0020-7462(82)90014-2
F.M. Atay, VAN DER POL'S OSCILLATOR UNDER DELAYED FEEDBACK Journal of Sound and Vibration. ,vol. 218, pp. 333- 339 ,(1998) , 10.1006/JSVI.1998.1843
S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, Optimization by Simulated Annealing Science. ,vol. 220, pp. 671- 680 ,(1983) , 10.1126/SCIENCE.220.4598.671
Junaid Ali Khan, Muhammad Asif Zahoor Raja, Ijaz Mansoor Qureshi, Stochastic Computational Approach for Complex Nonlinear Ordinary Differential Equations Chinese Physics Letters. ,vol. 28, pp. 020206- ,(2011) , 10.1088/0256-307X/28/2/020206
Kurt Hornik, Maxwell Stinchcombe, Halbert White, Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks Neural Networks. ,vol. 3, pp. 551- 560 ,(1990) , 10.1016/0893-6080(90)90005-6
Muhammad Asif Zahoor Raja, Junaid Ali Khan, Ijaz Mansoor Qureshi, A new stochastic approach for solution of Riccati differential equation of fractional order Annals of Mathematics and Artificial Intelligence. ,vol. 60, pp. 229- 250 ,(2010) , 10.1007/S10472-010-9222-X
A.J. Meade, A.A. Fernandez, The numerical solution of linear ordinary differential equations by feedforward neural networks Mathematical and Computer Modelling. ,vol. 19, pp. 1- 25 ,(1994) , 10.1016/0895-7177(94)90095-7
Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, Edward Teller, Equation of State Calculations by Fast Computing Machines The Journal of Chemical Physics. ,vol. 21, pp. 1087- 1092 ,(1953) , 10.1063/1.1699114