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The first step is to determine the value of the slow variable forcell i when cell i jumps down.
We claim that there exist uniqueconstants s i ∗ so that cell i jumps down when s i = s i ∗ ; see Figure 2, where s 1 ∗ = h ∗, s 2 ∗ = m 2 ∗ and s 3 ∗ = m 3 ∗.
Taking the example as a starting point, the present paper has relaxed the standard assumptions by considering well-behaved decision profiles, those such that: (i) jumps in q just occur on intervals all of whose points are points of strict monotonicity, and: (ii) intervals of singularity for q cannot contain points of strict monotonicity.
If cell i jumps down at time 0 and the inputs to the map specify that cellj jumps next, then the location of the coordinate determined by theoutputs of Π i j, relative to the curve C i k, determines whether cell i or cell k will followcell j into the active phase.
If, at some time,cell i jumps down and cell k jumps up, then we will define a map Π i k from the ( s j, s k ) phase plane to the ( s i, s j ) phase plane that gives the position of ( s i, s j ) when cell k jumps down.
Denoting the first term in the RHS of Eq. (6) as d i and the second term as d i,0 which is assumed to be a constant, we have When the variation of FP cavity length is large such that ϕ i jumps from -π/2 directly to π/2 or from π/2 directly to -π/2 a phase unwrapping technique can be used to obtain continuous phase or displacement [ 21].
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