Abstract: In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.
Abstract: In this paper, delay-dependent stability analysis for
neutral type neural networks with uncertain paramters and
time-varying delay is studied. By constructing new
Lyapunov-Krasovskii functional and dividing the delay interval into
multiple segments, a novel sufficient condition is established to
guarantee the globally asymptotically stability of the considered
system. Finally, a numerical example is provided to illustrate the
usefulness of the proposed main results.
Abstract: In this paper, we propose synchronization of an array of nonlinear systems with time delays. The array of systems is decomposed into isolated systems to establish appropriate Lyapunov¬Krasovskii functional. Using the Lyapunov-Krasovskii functional, a sufficient condition for the synchronization is derived in terms of LMIs(Linear Matrix Inequalities). Delayed feedback control gains are obtained by solving the sufficient condition. Numerical examples are given to show the validity the proposed method.
Abstract: In this paper, by employing a new Lyapunov functional
and an elementary inequality analysis technique, some sufficient
conditions are derived to ensure the existence and uniqueness of
periodic oscillatory solution for fuzzy bi-directional memory (BAM)
neural networks with time-varying delays, and all other solutions of
the fuzzy BAM neural networks converge the uniqueness periodic
solution. These criteria are presented in terms of system parameters
and have important leading significance in the design and applications
of neural networks. Moreover an example is given to illustrate the
effectiveness and feasible of results obtained.
Abstract: Many recent electrophysiological studies have
revealed the importance of investigating meditation state in order to
achieve an increased understanding of autonomous control of
cardiovascular functions. In this paper, we characterize heart rate
variability (HRV) time series acquired during meditation using
nonlinear dynamical parameters. We have computed minimum
embedding dimension (MED), correlation dimension (CD), largest
Lyapunov exponent (LLE), and nonlinearity scores (NLS) from HRV
time series of eight Chi and four Kundalini meditation practitioners.
The pre-meditation state has been used as a baseline (control) state to
compare the estimated parameters. The chaotic nature of HRV during
both pre-meditation and meditation is confirmed by MED. The
meditation state showed a significant decrease in the value of CD and
increase in the value of LLE of HRV, in comparison with premeditation
state, indicating a less complex and less predictable nature
of HRV. In addition, it was shown that the HRV of meditation state
is having highest NLS than pre-meditation state. The study indicated
highly nonlinear dynamic nature of cardiac states as revealed by
HRV during meditation state, rather considering it as a quiescent
state.
Abstract: This paper describes vibration analysis using the finite
element method for a small earphone, especially for the diaphragm
shape with a low-rigidity. The viscoelastic diaphragm is supported by
multiple nonlinear concentrated springs with linear hysteresis
damping. The restoring forces of the nonlinear springs have cubic
nonlinearity. The finite elements for the nonlinear springs with
hysteresis are expressed and are connected to the diaphragm that is
modeled by linear solid finite elements in consideration of a complex
modulus of elasticity. Further, the discretized equations in physical
coordinates are transformed into the nonlinear ordinary coupled
equations using normal coordinates corresponding to the linear natural
modes. We computed the nonlinear stationary and non-stationary
responses due to the internal resonance between modes with large
amplitude in the nonlinear springs and elastic modes in the diaphragm.
The non-stationary motions are confirmed as the chaos due to the
maximum Lyapunov exponents with a positive number. From the time
histories of the deformation distribution in the chaotic vibration, we
identified nonlinear modal couplings.
Abstract: In this paper, a fuzzy controller is designed for
stabilization of the Lorenz chaotic equations. A simple Mamdani
inference method is used for this purpose. This method is very simple
and applicable for complex chaotic systems and it can be
implemented easily. The stability of close loop system is investigated
by the Lyapunov stabilization criterion. A Lyapunov function is
introduced and the global stability is proven. Finally, the
effectiveness of this method is illustrated by simulation results and it
is shown that the performance of the system is improved.
Abstract: In this paper, we consider the uniform asymptotic stability, global asymptotic stability and global exponential stability of the equilibrium point of discrete Hopfield neural networks with delays. Some new stability criteria for system are derived by using the Lyapunov functional method and the linear matrix inequality approach, for estimating the upper bound of Lyapunov functional derivative.
Abstract: This article presents a detailed analysis and comparative
performance evaluation of model reference adaptive control systems.
In contrast to classical control theory, adaptive control methods allow
to deal with time-variant processes. Inspired by the works [1] and
[2], two methods based on the MIT rule and Lyapunov rule are
applied to a linear first order system. The system is simulated and
it is investigated how changes to the adaptation gain affect the
system performance. Furthermore, variations in the reference model
parameters, that is changing the desired closed-loop behaviour are
examinded.
Abstract: Daily production of information and importance of the sequence of produced data in forecasting future performance of market causes analysis of data behavior to become a problem of analyzing time series. But time series that are very complicated, usually are random and as a result their changes considered being unpredictable. While these series might be products of a deterministic dynamical and nonlinear process (chaotic) and as a result be predictable. Point of Chaotic theory view, complicated systems have only chaotically face and as a result they seem to be unregulated and random, but it is possible that they abide by a specified math formula. In this article, with regard to test of strange attractor and biggest Lyapunov exponent probability of chaos on several foreign exchange rates vs. IRR (Iranian Rial) has been investigated. Results show that data in this market have complex chaotic behavior with big degree of freedom.
Abstract: In this paper, the C1-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes.
Abstract: The problem of exponential stability and periodicity for a class of cellular neural networks (DCNNs) with time-varying delays is investigated. By dividing the network state variables into subgroups according to the characters of the neural networks, some sufficient conditions for exponential stability and periodicity are derived via the methods of variation parameters and inequality techniques. These conditions are represented by some blocks of the interconnection matrices. Compared with some previous methods, the method used in this paper does not resort to any Lyapunov function, and the results derived in this paper improve and generalize some earlier criteria established in the literature cited therein. Two examples are discussed to illustrate the main results.
Abstract: In this paper, we consider a food-limited population model with delay and feedback control. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.
Abstract: This paper addresses the problem of the partial state
feedback stabilization of a class of nonlinear systems. In order to
stabilization this class systems, the especial place of this paper is
to reverse designing the state feedback control law from the method
of judging system stability with the center manifold theory. First of
all, the center manifold theory is applied to discuss the stabilization
sufficient condition and design the stabilizing state control laws for a
class of nonlinear. Secondly, the problem of partial stabilization for a
class of plane nonlinear system is discuss using the lyapunov second
method and the center manifold theory. Thirdly, we investigate specially
the problem of the stabilization for a class of homogenous plane
nonlinear systems, a class of nonlinear with dual-zero eigenvalues and
a class of nonlinear with zero-center using the method of lyapunov
function with homogenous derivative, specifically. At the end of this
paper, some examples and simulation results are given show that the
approach of this paper to this class of nonlinear system is effective
and convenient.
Abstract: This study is concerned with a new adaptive impedance control strategy to compensate for unknown time-varying environment stiffness and position. The uncertainties are expressed by Function Approximation Technique (FAT), which allows the update laws to be derived easily using Lyapunov stability theory. Computer simulation results are presented to validate the effectiveness of the proposed strategy.
Abstract: This paper addresses the stability of the switched systems with discrete and distributed time delays. By applying Lyapunov functional and function method, we show that, if the norm of system matrices Bi is small enough, the asymptotic stability is always achieved. Finally, a example is provided to verify technically feasibility and operability of the developed results.
Abstract: In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given to show the effectiveness of the approach presented in this paper.