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Data from days spanning the transition from synchronizing to free running conditions or prior to stable synchronization were excluded from the activity profile analyses.
In the bistable states, where two asymmetric periodic attractors co-exist, it is shown that the coupled pendula can attain multistable states via a new dynamical transition the basin crisis that occur prior to the on-set of stable synchronization.
An indirect approach to adaptive interval type-2 fuzzy sliding mode control is proposed for the stable synchronization of two different chaotic nonlinear systems with different initial conditions under the presence of uncertainties involving process noises and external disturbances.
Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem, and the numerical simulations are performed to verify the effectiveness of presented schemes.
A modified adaptive control scheme is proposed to achieve globally asymptotic stable synchronization between the master and slave oscillators with arbitrary different initial conditions based on the Barbalat's Lemma.
Based on Lyapunov theory, linear matrix inequality (LMI) and linear matrix equality (LME) formulation, the output feedback controller is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an H∞-norm constraint.
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The sufficient condition of stable asymptotic synchronization and the boundary of feedback gain are given, based on the linear stability theorem.
then the dynamical networks (4) is exponentially stable, then exponential synchronization of the controlled dynamical networks (1) is achieved.
Using the master stability function approach, we derive the regime of coupling parameters leading to stable and unstable synchronization phenomena in the ring.
Therefore, in this case, system (13) is exponentially stable and the synchronization of the drive system (12) and the response system (11) sufficiently achieved.
It is clear that, if the zero solutions of the dynamical network (4) and (5) are globally exponentially stable, then exponential synchronization of the controlled dynamical network (1) is achieved.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com