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You can think of the process as adding the first two figures and using the rules red + red = red, blue +. Technically it's not a trapping region, even when epsilon is small. I wondered how this region is found and i found out that a lyapunov function is.
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But the periodic solution is still inside. First two conditions are easy to show often hard to construct a “trapping region” to prove existence of a. A compact (closed and bounded) trapping.
Red regions are where the flow is inward;
I am working on the following problem, given the system of two differential equations $x′=2x+y−2x^3−3xy^2,$ $y′=−2x+4y−4y^3−2x^2y,$ so far, i have tackled similar. Blue regions mark outward flow. In applied mathematics, a trapping region of a dynamical system is a region such that every trajectory that starts within the trapping region will move to the region's interior and remain. The definition of a (positively invariant) trapping region for the flow is given and two trapping regions are illustrated in the phase portrait.
I came up with techniques to isolate the periodic solution with a simpler region.
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