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

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

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

4. 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

5. Steady state & Stability