12 research outputs found
Complex-valued wavelet network
AbstractIn this paper, a complex-valued wavelet network (CWN) is proposed. The network has complex inputs, outputs, connection weights, dilation and translation parameters, but the nonlinearity of the hidden nodes remains a real-valued function (real-valued wavelet function). This kind of network is able to approximate an arbitrary nonlinear function in complex multi-dimensional space, and it provides a powerful tool for nonlinear signal processing involving complex signals. A complex algorithm is derived for the training of the proposed CWN. A numerical example on nonlinear communication channel identification is presented for illustration
Hopf Bifurcation and Chaos in Tabu Learning Neuron Models
In this paper, we consider the nonlinear dynamical behaviors of some tabu
leaning neuron models. We first consider a tabu learning single neuron model.
By choosing the memory decay rate as a bifurcation parameter, we prove that
Hopf bifurcation occurs in the neuron. The stability of the bifurcating
periodic solutions and the direction of the Hopf bifurcation are determined by
applying the normal form theory. We give a numerical example to verify the
theoretical analysis. Then, we demonstrate the chaotic behavior in such a
neuron with sinusoidal external input, via computer simulations. Finally, we
study the chaotic behaviors in tabu learning two-neuron models, with linear and
quadratic proximity functions respectively.Comment: 14 pages, 13 figures, Accepted by International Journal of
Bifurcation and Chao
Hopf Bifurcation and Chaos in a Single Inertial Neuron Model with Time Delay
A delayed differential equation modelling a single neuron with inertial term
is considered in this paper. Hopf bifurcation is studied by using the normal
form theory of retarded functional differential equations. When adopting a
nonmonotonic activation function, chaotic behavior is observed. Phase plots,
waveform plots, and power spectra are presented to confirm the chaoticity.Comment: 12 pages, 7 figure
Synchronization of fractional order chaotic systems
The chaotic dynamics of fractional order systems begin to attract much
attentions in recent years. In this brief report, we study the master-slave
synchronization of fractional order chaotic systems. It is shown that
fractional order chaotic systems can also be synchronized.Comment: 3 pages, 5 figure
Synchronization of two coupled fractional-order chaotic oscillators
Abstract The dynamics of fractional-order systems have attracted increasing attentions in recent years. In this paper, the synchronization of two coupled nonlinear fractional order chaotic oscillators is numerically demonstrated using the master-slave synchronization scheme. It is shown that fractional-order chaotic oscillators can be synchronized with appropriate coupling strength
A Note on Practical Stability of Nonlinear Vibration Systems with Impulsive Effects
This paper addresses the issue of vibration characteristics of nonlinear systems with impulsive
effects. By utilizing a T-S fuzzy model to represent a nonlinear system, a general strict practical
stability criterion is derived for nonlinear impulsive systems