ECE602 BME I Ordinary Differential Equations in Biomedical Engineering (cont’d)

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Presentation transcript:

ECE602 BME I Ordinary Differential Equations in Biomedical Engineering (cont’d)

Nonlinear ODEs Runge - Kutta of order 4 ( ): Single ODE

Nonlinear ODEs Runge - Kutta of order 4 ( ): Simultaneous ODEs

Steady state & Stability CaseReal PartImaginary PartStability 1All negativeZeroStable, nonoscillatory 2All negativeNonzeroStable, oscillatory 3All positiveZeroUnstable, nonoscillatory 4All positiveNonzeroUnstable, oscillatory 5Positive & negativeZeroMetastable, saddle point 6ZeroNonzeroNeutrally stable, oscillatory Stability Analysis Base on the Eigenvalues of the Jacobian Matrix

Steady state & Stability