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The mechanism of the famous phase compression is discussed, and it is used to control the chaos in the Hindmarsh-Rose (H-R) model. It is numerically confirmed that the phase compression scheme can be understood as one kind of intermittent feedback scheme, which requires appropriate thresholds and feedback coefficient, and the intermittent feedback can be realized with the Heaviside function. In the case of control chaos, the output variable (usually the voltage or the membrane potential of the neuron) is sampled and compared with the external standard signal of the electric electrode. The error between the sampled variable and the external standard signal of the electrode is input into the system only when the sampled variable surpasses the selected thresholds. The numerical simulation results confirm that the chaotic H-R system can be controlled to reach arbitrary n-periodical (n = 1, 2, 3, 4, 5, 6,...) orbit or stable state even when just one variable is feed backed into the system intermittently. The chaotic Chua circuit is also investigated to check its model independence and effectiveness of the schemes and the equivalence of the two schemes are confirmed again.

In this paper, a spatial perturbation scheme is proposed to suppress the spiral wave in the modified Orengonator model, which is used to describe the chemical reaction in the light-sensitive media. The controllable external illumination Φ is perturbed with a spatial linear function. In our numerical simulation, the scheme is investigated by imposing the external controllable illumination on the space continuously and/or intermittently. The numerical simulation results confirm that the stable rotating spiral wave still can be removed with the scheme proposed in this paper even if the controllable Φ changed vs. time and space synchronously. Then the scheme is also used to control the spiral wave and turbulence in the modified Fitzhugh–Nagumo model. It is found that the scheme is effective to remove the sable rotating and meandering spiral wave but it costs long transient period and intensity of the gradient parameter to eliminate the spiral turbulence.

In this paper, a new scheme of spatial perturbation is proposed to stabilize the pattern in the oscillatory media, which could be described with the complex Ginzburg–Landau equation. The numerical simulation results confirm that the spiral wave, antispiral wave and spatiotemporal chaos in the complex Ginzburg–Landau equation could be suppressed, and the scheme is also discussed with the conservative field theory. Furthermore, the spatiotemporal noise is also introduced into the whole media, it just confirms that it is robust to the spatiotemporal noise.

The degenerate optical parametric oscillator (DOPO) is investigated. We introduced a normal Lorenz chaotic signal to adjust the amplitude and period of the input electric field in order to influence the dynamics of the time-dependent system. Our numerical simulation results based on the phase figures and Lyapunov exponents spectrum confirm that the characters of the DOPO are determined by the amplitude of the input field, and the system could be controlled to reach n-periodical (n = 1, 2, 3, 4, 5, etc.) orbit, chaotic and/ or hyperchaotic and stable state by using a modified scheme based on the self-adaptive stratagem.

We investigate the noise-induced synchronization between two identical uncoupled Hodgkin–Huxley neurons with sinusoidal stimulations. The numerical results confirm that the value of critical noise intensity for synchronizing two systems is much less than the magnitude of mean size of the attractor in the original system, and the deterministic feature of the attractor in the original system remains unchanged. This finding is significantly different from the previous work [Phys. Rev. E 67 (2003) 027201] in which the value of the critical noise intensity for synchronizing two systems was found to be roughly equal to the magnitude of mean size of the attractor in the original system, and at this intensity, the noise swamps the qualitative structure of the attractor in the original deterministic systems to synchronize to their stochastic dynamics. Further investigation shows that the critical noise intensity for synchronizing two neurons induced by noise may be related to the structure of interspike intervals of the original systems.

A study of Hodgkin–Huxley (HH) neuron under external sinusoidal excited stimulus is presented in this paper. As is well known, the stimulus frequency is to be considered as a bifurcate parameter and numerous phenomena, such as synchronization, period and chaos appear alternatively with the changing of the stimulus frequency. For the stimulus frequency less than 2fB (fB being the base frequency in this paper), the simulation results demonstrate that the single HH neuron could completely convey the sinusoidal signal in anti-phase into interspike interval (ISI) sequences. We also report, perhaps for the first time, another kind of phenomenon, the beat phenomenon, which exists in the phase dynamics of the ISI sequences of the HH neuron stimulated by a sinusoidal current. It is shown furthermore that intermittent transition results in the general route to chaos.

Based on the analysis of notch-root stresses and strains in bodies subjected to multiaxial loading, a quantitative relationship between Neuber rule and the equivalent strain energy density method is found. In the case of elastic range, both Neuber rule and the equivalent strain energy density method get the same estimation of the local stresses and strains. Whereas in the case of elastic-plastic range, Neuber rule generally overestimates the notch-root stresses and strains and the equivalent strain energy density method tends to underestimate the notch-root stresses and strains. A modified method is presented considering the material constants of elastic-plastic Poisson's ratio, elastic modulus, shear elastic modulus, and yield stress. The essence of the modified model is to add a modified coefficient to Neuber rule, which makes the calculated results tend to be more precise and reveals its energy meaning. This approach considers the elastic-plastic properties of the material itself and avoids the blindness of selecting coefficient values. Finally the calculation results using the modified model are validated with the experimental data.

Based on the principle of parallax of binocular visual system, three-dimensional of target is acquired by a lot of images. One identification technique for three-dimensional (3D) target is proposed in this paper. The characteristic information of target is extracted and reconstructed after images which are collected in OpenCV are pre-processed; Finally, based on Support Vector Machine package, the target system is distinguished by comparing characteristic and template.

Based on the Lyapunov stability theory, the Lyapunov function in the form of exponential type is constructed. The four-variable Chen hyperchaotic model is investigated as an example. The reliability of a linear coupling-inudced synchronization of hyperchaotic system is proofed analytically. Furthermore, the modulation effect of nonlinear coupling on the synchronization induced by linear coupling is investigated. A statictical function is defined to evaulate the power consumption of controller according to the dimensionaless dynamical equations, the appropriate parameter region for synchronization due to the joint action of linear and nonlinear coupling, and the extensive numerical results confirm the correctress of the theoretical predication.

We investigated the external electric field-induced transition of the spiral wave and turbulence in a class of time-varied reaction-diffusion systems. In our numerical simulation, a modified Fitzhugh-Nagumo model, which was used to describe the excitable and/or oscillatory media under appropriate parameters, was investigated. The effect induced by the random and/or other uncertain factors (for example, external and interior noise, gas pressure, temperature gradient and deformation of media etc.) was considered. The amplitude of the fluctuations of parameters was selected at appropriate values so that stable rotating spiral wave, meandering spiral wave and turbulence could be observed respectively. The external electric field was introduced into the media after a transient period allowing for parameter fluctuations. It was found that only the breakup of spiral wave was observed and the whole media could not reach homogeneous state when weak electric field and parameter fluctuation were used. It was confirmed that the breakup of spiral wave happens and then the whole media becomes stably homogeneous when appropriately strong intensity of external electric field is applied to the whole media together with the action of parameter fluctuation. The snapshots of the activator are used to investigate the transition of the patterns in the presence of external electric field and under parameter fluctuation, and relevant theoretical discussion is given in the precent paper.

A new scheme is proposed to suppress the meandering spiral waves in the excitable media, which is described with two-dimensional variables. An external electronic signal with stochastic phase is imposed on a local area; few grids of the system are perturbed, for example, 4×4 and/or 5×5 grid nodes among all the 256×256 nodes, so that a new target wave may occur and competition between the newly generated target wave and the intrinsic meandering spiral waves develops dynamically. The numerical simulation results confirm that it is effective to suppress the meandering spiral wave in the Barkley model. Compared with a simple periodical driving in a local area, it shows some advantages such as shorter transient period to kill the spiral wave, and it is robust to spatiotempaoral noise. A new target wave could come into being and will kill the meandering spiral wave even in the anisotropic media,of which the diffusion coefficient is a function of space, when the intensity of the spatiotemporal noise is not too strong.

Modulating the current input of two uncoupled Hindmarsh-Rose neurons by using the membrane potential of Hindmarsh-Rose neuron under different initial conditions, the evolution mechanism of synchronization process of the two neurons is revealed by analyzing interspike interval sequences. When periodic stimulation is u sed, the full synchronization is realized in two identical neurons, and the sync hronized response of modulated neurons can be different from the stimulation sig nal; and phase synchronization can be obtained in two neurons with different par ameters:two neurons with small parameter mismatch can be synchronized to the per iodic response different from the stimulation signal, and two neurons with big p arameter mismatch can only be synchronized to the response in phase synchronizat ion with stimulation signal. When chaotic stimulation is used, two systems can o nly be synchronized to the response being in phase synchronization with stimulat ion signal. Obviously, chaotic stimulation is more helpful in encoding and deco ding information. Analyzing the relation between the largest condition Lyapunov exponents and the stimulation strength shows that when the largest condition Lya punov exponents of the two systems are both negative is the necessary condition for synchronization. The chaotic stimulation signal can more easily synchronize two neurons than periodic stimulation signal, implying that the effect of chaoti c stimulation is stronger than periodic one, and the experiments also confirm th is conclusion.