Bifurcations and excitability in the temperature-sensitive Morris–Lecar neuron

Nonlinear Dynamics - The neuronal excitability related to the transition between firing and resting states is a basic and important dynamic behavior which has different bifurcation characteristics...     

Synchronization mode transitions induced by chaos in modified Morris–Lecar neural systems with weak coupling

Nonlinear Dynamics - Based on a modified Morris–Lecar neural model, the synchronization modes transitions between two coupled neurons or star-coupled neural network connected by weak...     

Robust adaptive sliding mode control for synchronization of space-clamped FitzHugh–Nagumo neurons

Unlike taking the same external electrical stimulation to discuss chaotic synchronization in the literature, the synchronization between two uncouple FitzHugh?CNagumo (FHN) neurons with different ionic currents and external electrical stimulations is considered. The main contribution of this study is the application of a robust adaptive sliding-mode controller instead of the active elimination. The proposed sliding mode controller associated with time varying feedback gains cannot only tackle the system uncertainties and external disturbances, but also compensate for the mismatch nonlinear dynamics of synchronized error system without direct cancellation. Meanwhile, these feedback gains are not determined in advance but updated by the adaptive laws. Sufficient conditions to guarantee the stable synchronization are given in the sense of the Lyapunov stability theorem. In addition, numerical simulations are also performed to verify the effectiveness of presented scheme.     

Stability properties of a two-dimensional system involving one Caputo derivative and applications to the investigation of a fractional-order Morris–Lecar neuronal model

Adaptive infinite impulse response filters have received much attention due to its utilization in a wide range of real-world applications. The design of the IIR filters poses a typically nonlinear, non-differentiable and multimodal problem in the estimation of the coefficient parameters. The aim of the current study is the application of a novel hybrid optimization technique based on the combination of cellular particle swarm optimization and differential evolution called CPSO–DE for the optimal parameter estimation of IIR filters. DE is used as the evolution rule of the cellular part in CPSO to improve the performance of the original CPSO. Benchmark IIR systems commonly used in the specialized literature have been selected for tuning the parameters and demonstrating the effectiveness of the CPSO–DE method. The proposed CPSO–DE method is experimentally compared with two new design methods: the tissue-like membrane system (TMS), the hybrid particle swarm optimization and gravitational search algorithm (HPSO–GSA), the original CPSO-outer and CPSO-inner, and classical implementations of PSO, GSA and DE. Computational results and comparison of CPSO–DE with the other evolutionary and hybrid methods show satisfactory results. The hybridization of CPSO and DE demonstrates powerful estimation ability. In particular, to our knowledge, this hybridization has not yet been investigated for the IIR system identification.     

Multiple synchronization transitions due to periodic coupling strength in delayed Newman–Watts networks of chaotic bursting neurons

In this paper, we numerically study the effect of time-periodic coupling strength on the synchronization of firing activity in delayed Newman–Watts networks of chaotic bursting neurons. We first examine how the firing synchronization transitions induced by time delay under fixed coupling strength changes in the presence of time-periodic coupling strength, and then focus on how time-periodic coupling strength induces synchronization transitions in the networks. It is found that time delay can induce more synchronization transitions in the presence of time-periodic coupling strength compared to fixed coupling strength. As the frequency of time-periodic coupling strength is varied, the firing exhibits multiple synchronization transitions between spiking antiphase synchronization and in-phase synchronization of various firing behaviors including bursting, spiking, and both bursting and spiking, depending on the values of time delay. These results show that time-periodic coupling strength can increase the synchronization transitions by time delay and can induce multiple synchronization transitions of various firing behaviors in the neuronal networks. This means that time-periodic coupling strength plays an important role in the information processing and transmission in neural systems.     

High-order synchronization of stick–slip process: experiments on spring–slider system

In the last years it has been shown that the synchronization and triggering of dynamic events by weak external forcing is ubiquitous and is observed in biological systems, lasers, electronic networks, etc. In the present paper, new experimental data on the phase synchronization in frictional system induced by a weak electromagnetic or mechanical periodic forcing are analyzed. For quantitative analysis of stick–slip time series, modern tools of nonlinear dynamics were used. Stick–slip events were identified by recording acoustic emissions, which accompany slip displacements. The spring–slider system in stick–slip regime is considered as a proxy of active tectonic fault, generating earthquakes. The effect of high-order synchronization of stick–slip events by weak electromagnetic or mechanical periodic forcing, as well as the phenomenon of phase time delay of the synchronized slip events behind the forcing phase, was discovered. These findings can help to find new regularities in seismic time series.     

Achievement of chaotic synchronization trajectories of master–slave manipulators with feedback control strategy

This paper addresses a master-slave synchro- nization strategy for complex dynamic systems based on feedback control. This strategy is applied to 3-DOF pla- nar manipulators in order to obtain synchronization in such complicated as chaotic motions of end-effectors. A chaotic curve is selected from Duffing equation as the trajectory of master end-effector and a piecewise approximation method is proposed to accurately represent this chaotic trajectory of end-effectors. The dynamical equations of master-slave manipulators with synchronization controller are derived, and the Lyapunov stability theory is used to determine the stability of this controlled synchronization system. In numer- ical experiments, the synchronous motions of end-effectors as well as three joint angles and torques of master-slave manipulators are studied under the control of the proposed synchronization strategy. It is found that the positive gain matrix affects the implementation of synchronization con- trol strategy. This synchronization control strategy proves the synchronization＇s feasibility and controllability for com- plicated motions generated by master-slave manipulators.     

Adaptive synchronization of time delay Hindmarsh–Rose neuron system via self-feedback

Synchronization of two mismatched time delay Hindmarsh?CRose neuron systems with self-feedback is investigated. Based on the Lyapunov stability theory and the adaptive control theory, a linear adaptive feedback controller and parameter estimation update law are proposed, and the sufficient conditions for synchronization of the two mismatched systems with chaotic bursting behavior are obtained. The correctness of the proposed methods is rigorously demonstrated. Finally, numerical simulations are employed to verify the effectiveness of the proposed scheme.     

Pattern dynamics of a spatial predator–prey model with noise

A spatial predator–prey model with colored noise is investigated in this paper. We find that the number of the spotted pattern is increased as the noise intensity is increased. When the noise intensity and temporal correlation are in appropriate levels, the model exhibits phase transition from spotted to stripe pattern. Moreover, we show the number of the spotted and stripe pattern, with respect to both noise intensity and temporal correlation. These studies raise important questions on the role of noise in the pattern formation of the populations, which may well explain some data obtained in the ecosystems.     

Experimental study of vortex–structure interaction noise radiated from rod–airfoil configurations

Vortex–structure interaction noise radiated from an airfoil embedded in the wake of a rod is investigated experimentally in an anechoic wind tunnel by means of a phased microphone array for acoustic tests and particle image velocimetry (PIV) for the flow field measurements. The rod–airfoil configuration is varied by changing the rod diameter (D), adjusting the cross-stream position (Y) of the rod and the streamwise gap (L) between the rod and the airfoil leading edge. Two noise control concepts, including “air blowing” on the upstream rod and a soft-vane leading edge on the airfoil, are applied to control the vortex–structure interaction noise. The motivation behind this study is to investigate the effects of the three parameters on the characteristics of the radiated noise and then explore the influences of the noise control concepts. Both the vortex–structure interaction noise and the rod vortex shedding tonal noise are analysed. The acoustic test results show that both the position and magnitude of the dominant noise source of the rod–airfoil model are highly dependent on the parameters considered. In the case where the vortex–structure interaction noise is dominant, the application of the air blowing and the soft vane can effectively attenuate the interaction noise. Flow field measurements suggest that the intensity of the vortex–structure interaction and the flow impingement on the airfoil leading edge are suppressed by the control methods, giving a reduction in noise.     

Application of Takagi–Sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization

In this study, we investigate a class of chaotic synchronization and anti-synchronization with stochastic parameters. A controller is composed of a compensation controller and a fuzzy controller which is designed based on fractional stability theory. Three typical examples, including the synchronization between an integer-order Chen system and a fractional-order Lü system, the anti-synchronization of different 4D fractional-order hyperchaotic systems with non-identical orders, and the synchronization between a 3D integer-order chaotic system and a 4D fractional-order hyperchaos system, are presented to illustrate the effectiveness of the controller. The numerical simulation results and theoretical analysis both demonstrate the effectiveness of the proposed approach. Overall, this study presents new insights concerning the concepts of synchronization and anti-synchronization, synchronization and control, the relationship of fractional and integer order nonlinear systems.     

Adaptive synchronization of chaotic Cohen–Crossberg neural networks with mixed time delays

In this paper, the problem of adaptive synchronization is investigated for a class of Cohen–Crossberg neural networks with mixed time delays. Based on a Lyapunov–Krasovskii functional and the invariant principle of function differential equations as well as the adaptive control and linear feedback with update law, a linear matrix inequality approach is developed to derive some novel sufficient conditions achieving synchronization of the two coupled networks with mixed time delays. In particular, the mixed time delays in this paper synchronously consist of constant delays, time-varying delays, and distributed delays, which are more general than those discussed in the previous literature. Therefore, the results obtained in this paper comprise and generalize those given in the previous literature. A numerical example and its simulation are provided to show the effectiveness of the theoretical results.     

Adaptive regulation synchronization for a class of delayed Cohen–Grossberg neural networks

This paper presents a new approach to asymptotic synchronization problems based on regulation of connection weights for a class of Cohen–Grossberg neural networks with bounded time-varying delays. By using the adaptive technique, this approach requires no information about weights and bounds of amplification and activation functions, as well as the bounds of time-delays. As opposed to other existing methods, the adverse effects of delays can be completely eliminated by regulating weights and without using any control inputs. Through Lyapunov functions and adaptive schemes, we prove the regulation laws can ensure the neural network asymptotically synchronize to the targeted equilibrium point. The proposed theoretical result is finally evaluated in the light of a simulation example.     

Impact of noise on pattern formation in a predator–prey model

In this paper, we investigated the influence of color noise on pattern formation in a predator–prey model. When the model has no noise, it exhibits wave dynamics. A series of numerical simulations showed that break-up of waves will emerge when noise is added. Furthermore, stationary pattern can be induced by noise. The obtained results may point out that noise can have great effect on spatial complexity of ecosystems.     

Synchronization and chimeras in a network of photosensitive FitzHugh–Nagumo neurons

Nonlinear Dynamics - Recently, a photosensitive model has been proposed that takes into account nonlinear encoding and responses of photosensitive neurons that are subject to optical signals. In...     

The formation of hydrodynamic slugs by the interaction of waves in gas–liquid two-phase pipe flow

This paper examines the effects of wave interaction on the formation of hydrodynamic slugs in two-phase pipe flow at relatively low gas and liquid superficial velocities. The experiments were conducted using a horizontal 31 m long, D = 10 cm internal diameter transparent pipe at atmospheric pressure. High resolution photography allowed the location of the gas–liquid interface to be measured with a high degree of accuracy at 5 Hz. Image analysis allowed individual waves to be tracked over a 14D section of the pipe. Regular waves having similar properties such as speed, amplitude and length were seen far from the region of slug formation. However, near the transition region, where hydrodynamic slugs were formed, significant differences between wave properties were observed which resulted in wave interaction leading to a type of sub-harmonic resonance and slug formation. The formation of hydrodynamic slugs due to wave interaction differs from predictions for slug formation using long wavelength stability theory. The properties of the waves were quantified which gave detailed information on the resonance mechanism found near the transition to slugging.