We propose a modified Fitzhugh-Nagumo neuron(MFNN) model. Based on this model, an integerorder MFNN system(case A) and a fractional-order MFNN system(case B) were investigated. In the presence of electromagnetic induc...We propose a modified Fitzhugh-Nagumo neuron(MFNN) model. Based on this model, an integerorder MFNN system(case A) and a fractional-order MFNN system(case B) were investigated. In the presence of electromagnetic induction and radiation, memductance and induction can show a variety of distributions. Fractionalorder magnetic flux can then be considered. Indeed, a fractional-order setting can be acceptable for non-uniform diffusion. In the case of an MFNN system with integer-order discontinuous magnetic flux, the system has chaotic and non-chaotic attractors. Dynamical analysis of the system shows the birth and death of period doubling, which is a sign of antimonotonicity. Such a behavior has not been studied previously in the dynamics of neurons. In an MFNN system with fractional-order discontinuous magnetic flux, different attractors such as chaotic and periodic attractors can be observed. However, there is no sign of antimonotonicity.展开更多
We explain the functional projective lag synchronization of a hyperchaotic Rossler system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. ...We explain the functional projective lag synchronization of a hyperchaotic Rossler system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. Based on Lyapunov stability theory, an active control method and adaptive control law are employed to make the states of two hyperchaotic Rossler systems asymptotically synchronized. Finally, some numerical examples are provided to show the effectiveness of our results.展开更多
In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities ...In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities （LMIs） by constructing new Lyapunov-Krasovskii functional. The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints. The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound. Numerical examples are presented to show the effectiveness of the proposed method.展开更多
We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov-Krasovskii functional combined with the...We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov-Krasovskii functional combined with the input delay approach and some inequality techniques to derive sufficient conditions that ensure the exponential synchronization of the delayed neural network. The conditions are formulated in terms of the leakage delay, the sampling period, and the exponential convergence rate. Numerical examples are given to demonstrate the usefulness and the effectiveness of the results.展开更多
文摘We propose a modified Fitzhugh-Nagumo neuron(MFNN) model. Based on this model, an integerorder MFNN system(case A) and a fractional-order MFNN system(case B) were investigated. In the presence of electromagnetic induction and radiation, memductance and induction can show a variety of distributions. Fractionalorder magnetic flux can then be considered. Indeed, a fractional-order setting can be acceptable for non-uniform diffusion. In the case of an MFNN system with integer-order discontinuous magnetic flux, the system has chaotic and non-chaotic attractors. Dynamical analysis of the system shows the birth and death of period doubling, which is a sign of antimonotonicity. Such a behavior has not been studied previously in the dynamics of neurons. In an MFNN system with fractional-order discontinuous magnetic flux, different attractors such as chaotic and periodic attractors can be observed. However, there is no sign of antimonotonicity.
文摘We explain the functional projective lag synchronization of a hyperchaotic Rossler system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. Based on Lyapunov stability theory, an active control method and adaptive control law are employed to make the states of two hyperchaotic Rossler systems asymptotically synchronized. Finally, some numerical examples are provided to show the effectiveness of our results.
基金Project supported by the Daegu University Research Grant,2009
文摘In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities （LMIs） by constructing new Lyapunov-Krasovskii functional. The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints. The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound. Numerical examples are presented to show the effectiveness of the proposed method.
基金supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(Grant No.2013R1A1A2A10005201)the UAE University(Grant No.NRF Project UAEU-NRF-7-20886)
文摘We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov-Krasovskii functional combined with the input delay approach and some inequality techniques to derive sufficient conditions that ensure the exponential synchronization of the delayed neural network. The conditions are formulated in terms of the leakage delay, the sampling period, and the exponential convergence rate. Numerical examples are given to demonstrate the usefulness and the effectiveness of the results.
