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This difference was clearer in nonlinear master curves.
Backbone relaxation times (τb) from nonlinear master curves almost coincided with linear viscoelastic terminal relaxation times (τw) from linear master curves within the limits imposed by experimental error.
In nonlinear master curves (Q0, linear PIs showed only one peak corresponding to relaxation of the backbone chain, whereas two weak local peaks were observed for 3-arm star PIs.
Based on the hierarchical relaxation concept of branched polymers, three characteristic relaxation times of 3-arm star PIs were determined from a nonlinear master curve: backbone relaxation time (τb) from local maximum Q0 at lower frequency, backbone Rouse time (τR,b) from local minimum Q0, and arm relaxation time (τa) from local maximum Q0 at higher frequency.
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Assumption 1 Assume that the nonlinear functions in master-slave system (1) are bounded, i.e., there exist two constants M f ≥ 0 and M g ≥ 0 such that ∥ f ( x ( t ), t ) ∥ ∞ ≤ M f, ∥ g ( y ( t ), t ) ∥ ∞ ≤ M g. hold for any x ( t ), y ( t ) ∈ R n and t > 0. Remark 3 There exist a lot of papers that study the synchronization problems of master-slave chaotic systems.
A special attention is paid to the algorithms for the core optimizers intervening in the master and slave nonlinear programming problems resulting from OPF decomposition.
The master system is any smooth nonlinear chaotic system, while the slave system is a nonlinear chaotic system in the feedback form.
In this article a global method for master-slave synchronization of nonlinear systems is provided.
Different from some existing master-slave models, the nonlinear terms in the considered chaotic system only need to satisfy bounded conditions.
Because of its flexibility, it can be used in many different nonlinear control courses, both in undergraduate and master courses.
In this paper, master-slave synchronization methods for nonlinear system are proposed under a reliable control scheme.
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