Equation

Sinusoidal Integration 2

$$\left\{ \begin{array}{lll}\dot{x}_{1} & = & 1\\\dot{x}_{2} & = & -a\cdot x_{2}+(a-1)\cdot\sin(x_{1})+(1-a)\cdot\cos(x_{1})\end{array}\right.$$

Initial set: $(x_{1}-1)^{2}+(x_{2}-1)^{2}\leq 1$ and $a=10$

Search space: $[-0.1, 8]\times[-3,3]$

Figure

Code

from pyinvariant import *

# Define the search space
space = IntervalVector([[-0.1,8],[-3,3]])

# Create the grpah structure
smartSubPaving = SmartSubPaving(space)

# Create the Domain
dom_outer = Domain(smartSubPaving, FULL_WALL)
dom_outer.set_border_path_in(False)
dom_outer.set_border_path_out(False)
f_sep = Function("x[2]", "(x[0]-1)^2+(x[1]-1)^2-(1)^2")
s_outer = SepFwdBwd(f_sep, LEQ) # possible options : LT, LEQ, EQ, GEQ, GT
dom_outer.set_sep_input(s_outer);

dom_inner = Domain(smartSubPaving, FULL_DOOR)
dom_inner.set_border_path_in(True)
dom_inner.set_border_path_out(True)
s_inner = SepFwdBwd(f_sep, GEQ) # possible options : LT, LEQ, EQ, GEQ, GT
dom_inner.set_sep_output(s_inner);

# Create the Dynamics
f = Function("x[2]", "(1,-10*x[1]+(-1+10)*sin(x[0])+(1+10)*cos(x[0]))")
dyn = DynamicsFunction(f, FWD)

# Create the two Maze associated with the Domain and the dynamics
maze_inner = Maze(dom_inner, dyn)
maze_outer = Maze(dom_outer, dyn)

# Contract the system
for i in range(18):
	print(i)
	smartSubPaving.bisect()
	maze_outer.contract()
	maze_inner.contract()

# Visualization
visu = VibesMaze("Sinusoidal 2 Intergation", maze_outer, maze_inner)
visu.setProperties(0,0,512,512)
visu.show()
visu.drawCircle(1, 1, 1, "black[red]");