Block calculates numeric solution of a 2nd-order nonlinear autonomous system. The time interval in which the solution is calculated is specified by Simulink simulation parameters, however, if either NaN or Inf value is reached during the simulation, it is stopped immediately. The block is usually used in combination with the Vector XY Graph for Phase Portraits block that plots the calculated solution in phase plane, but it can also co-operate with other blocks (e.g. Selector or Scope) in order to treat phase trajectories individually.
Differential equation of a 2nd-order nonlinear autonomous system in symbolic form. The convention to write mathematical operations is the same as the one used by MATLAB's Symbolic Math Toolbox. System output is denoted as y.
Minimum and maximum values of initial conditions for the x1 coordinate (system output) corresponding to different trajectories. Together with the following parameter and analogical values for x2 these values determine the number of simultaneously running calculations i.e. the density of trajectories in phase plane.
Positive integer specifying the number of different initial conditions for the x1 coordinate; initial conditions are from the range specified by above parameters and are distributed uniformly.
Minimum and maximum values of initial conditions for the x2 coordinate (derivative of system output) corresponding to different trajectories. Together with the following parameter and analogical values for x1 these values determine the number of simultaneously running calculations i.e. the density of trajectories in phase plane.
Positive integer specifying the number of different initial conditions for the x2 coordinate; initial conditions are from the range specified by above parameters and are distributed uniformly.
Simulink scheme and phase-plane portrait of nonlinear autonomous system y''(t) + [y'(t)]2 = 0 with initial conditions being x1(0) = <-5; 5> (10 values) a x2(0) = <-1; 10> (3 values).
