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The trajectory of the model array represents the best fit to the observed pore water data (Figure 13).
The controllers are designed in such a way that after each time period T, the trajectory of the nonholonomic double integrator intersects the trajectory of the model reference, which can be made asymptotically stable.
Calculating the difference of V ( k ) along the trajectory of the model (18) and taking the mathematical expectation, one obtains E { Δ V ( k ) } = E { Δ V 1 ( k ) } + E { Δ V 2 ( k ) } + E { Δ V 3 ( k ) } + E { Δ V 4 ( k ) }, (37).
Each run of the simulation gives one possible trajectory of the model through state space.
The most probable path is the most likely trajectory of the model system to get from one state to another.
Each stochastic simulation represents one possible trajectory of the model (rather than average behaviour which is what the ODE analysis provides, in general).
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Mathematically, in order to find treatment strategies, we have to find the analytical conditions under which trajectories of the model will converge to infection-free equilibrium.
This guarantees that M lc is also transient for the trajectories of the model that coil around M lc while translating slowly towards the edge, which corresponds to the aforementioned homoclinic bifurcation.
A positive value of the LE indicates a chaotic irregular behavior whereby two trajectories of the model, which are subjected to identical noise and initially close to each other, diverge as time goes [45].
Trajectories of the model show quasi-chaotic behavior for a broad range of the model parameters.
(A ) Initial trajectories of the model head directly towards the peak probability of finding an odor source.
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