Study on Circle Maps Mechanism of Neural Spikes Sequence

Brain-machine interfaces (BMIs) decode cortical neural spikes of paralyzed patients to control external devices for the purpose of movement restoration. Neuroplasticity induced by conducting a relatively complex task within multistep, is helpful to performance improvements of BMI system. Reinforcement learning (RL) allows the BMI system to interact with the environment to learn the task adaptively without a teacher signal, which is more appropriate to the case for paralyzed patients. In this work, we proposed to apply Q(λ)-learning to multistep goal-directed tasks using users neural activity. Neural data were recorded from M1 of a monkey manipulating a joystick in a center-out task. Compared with a supervised learning approach, significant BMI control was achieved with correct directional decoding in 84.2% and 81% of the trials from naïve states. The results demonstrate that the BMI system was able to complete a task by interacting with the environment, indicating that RL-based methods have the potential to develop more natural BMI systems.

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GENERALIZED SYNCHRONIZATION, FREQUENCY-LOCKING AND PHASE-LOCKING OF COUPLED SINE CIRCLE MAPS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127401003280 ◽

2001 ◽

Vol 11 (08) ◽

pp. 2245-2253

Author(s):

WEN-XIN QIN

Keyword(s):

Dynamical Systems ◽

Invariant Manifold ◽

Coupling Strength ◽

Phase Locking ◽

Coupled System ◽

Generalized Synchronization ◽

Frequency Locking ◽

Local Systems ◽

Circle Maps ◽

The Individual

Applying invariant manifold theorem, we study the existence of generalized synchronization of a coupled system, with local systems being different sine circle maps. We specify a range of parameters for which the coupled system achieves generalized synchronization. We also investigate the relation between generalized synchronization, predictability and equivalence of dynamical systems. If the parameters are restricted in the specified range, then all the subsystems are topologically equivalent, and each subsystem is predictable from any other subsystem. Moreover, these subsystems are frequency locked even if the frequencies are greatly different in the absence of coupling. If the local systems are identical without coupling, then the widths of the phase-locked intervals of the coupled system are the same as those of the individual map and are independent of the coupling strength.

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SIMPLE AND COMPLEX DYNAMICS FOR ONE-DIMENSIONAL MANIFOLD MAPS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127495001022 ◽

1995 ◽

Vol 05 (05) ◽

pp. 1351-1355

Author(s):

VLADIMIR FEDORENKO

Keyword(s):

Topological Entropy ◽

Complex Dynamics ◽

Periodic Points ◽

Dimensional Manifold ◽

One Dimensional ◽

Circle Maps ◽

Interval Maps ◽

Chain Recurrent Set ◽

Recurrent Set

We give a characterization of complex and simple interval maps and circle maps (in the sense of positive or zero topological entropy respectively), formulated in terms of the description of the dynamics of the map on its chain recurrent set. We also describe the behavior of complex maps on their periodic points.

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