8,034 research outputs found
Adaptive hybrid function projective synchronization of chaotic systems with fully unknown periodical time-varying parameters
In this paper, an adaptive learning control approach is presented for the hybrid functional projective synchronization (HFPS) of different chaotic systems with fully unknown periodical time-varying parameters. Differential-difference hybrid parametric learning laws and an adaptive learning control law are constructed via the LyapunovâKrasovskii functional stability theory, which make the states of two different chaotic systems asymptotically synchronized in the sense of mean square norm. Moreover, the boundedness of the parameter estimates are also obtained. The Lorenz system and Chen system are illustrated to show the effectiveness of the hybrid functional projective synchronization scheme
On the validity of memristor modeling in the neural network literature
An analysis of the literature shows that there are two types of
non-memristive models that have been widely used in the modeling of so-called
"memristive" neural networks. Here, we demonstrate that such models have
nothing in common with the concept of memristive elements: they describe either
non-linear resistors or certain bi-state systems, which all are devices without
memory. Therefore, the results presented in a significant number of
publications are at least questionable, if not completely irrelevant to the
actual field of memristive neural networks
Neuronal synchrony: peculiarity and generality
Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their âdynamical repertoireâ includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neuronal networks with plastic synapses (synchronization with activity dependent coupling), (ii) synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks (partial synchronization of small composite structures), and (iv) coarse grained synchronization in larger systems (synchronization on a mesoscopic scale
Rhythmic dynamics and synchronization via dimensionality reduction : application to human gait
Reliable characterization of locomotor dynamics of human walking is vital to understanding the neuromuscular control of human locomotion and disease diagnosis. However, the inherent oscillation and ubiquity of noise in such non-strictly periodic signals pose great challenges to current methodologies. To this end, we exploit the state-of-the-art technology in pattern recognition and, specifically, dimensionality reduction techniques, and propose to reconstruct and characterize the dynamics accurately on the cycle scale of the signal. This is achieved by deriving a low-dimensional representation of the cycles through global optimization, which effectively preserves the topology of the cycles that are embedded in a high-dimensional Euclidian space. Our approach demonstrates a clear advantage in capturing the intrinsic dynamics and probing the subtle synchronization patterns from uni/bivariate oscillatory signals over traditional methods. Application to human gait data for healthy subjects and diabetics reveals a significant difference in the dynamics of ankle movements and ankle-knee coordination, but not in knee movements. These results indicate that the impaired sensory feedback from the feet due to diabetes does not influence the knee movement in general, and that normal human walking is not critically dependent on the feedback from the peripheral nervous system
Multiple chaotic central pattern generators with learning for legged locomotion and malfunction compensation
An originally chaotic system can be controlled into various periodic
dynamics. When it is implemented into a legged robot's locomotion control as a
central pattern generator (CPG), sophisticated gait patterns arise so that the
robot can perform various walking behaviors. However, such a single chaotic CPG
controller has difficulties dealing with leg malfunction. Specifically, in the
scenarios presented here, its movement permanently deviates from the desired
trajectory. To address this problem, we extend the single chaotic CPG to
multiple CPGs with learning. The learning mechanism is based on a simulated
annealing algorithm. In a normal situation, the CPGs synchronize and their
dynamics are identical. With leg malfunction or disability, the CPGs lose
synchronization leading to independent dynamics. In this case, the learning
mechanism is applied to automatically adjust the remaining legs' oscillation
frequencies so that the robot adapts its locomotion to deal with the
malfunction. As a consequence, the trajectory produced by the multiple chaotic
CPGs resembles the original trajectory far better than the one produced by only
a single CPG. The performance of the system is evaluated first in a physical
simulation of a quadruped as well as a hexapod robot and finally in a real
six-legged walking machine called AMOSII. The experimental results presented
here reveal that using multiple CPGs with learning is an effective approach for
adaptive locomotion generation where, for instance, different body parts have
to perform independent movements for malfunction compensation.Comment: 48 pages, 16 figures, Information Sciences 201
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