A further contribution to the modelling of multi-waveform generators

A method has been presented in recent papers for deriving precisely stabilized waveform generators by relating them to second-order conservative oscillators. The present paper suggests a method for considerably generalizing the previous class ofgenerator models. This should enable the development of a larger variety of waveform generators with ease and flexibility. The new method is analyzed and is shown to possess implications to theoretical biology and other fields.     

Robust synchronization of different coupled oscillators: Application to antenna arrays

This paper deals with the synchronization of a chain of nonlinear and uncertain models of nonidentical oscillators. Using Lyapunov's theory of stability, a dynamical controller guaranteeing the synchronization of the oscillators is determined. The problem of synchronization is transformed into a problem of asymptotic stabilization for a nonlinear system and then is formulated as a system of linear matrix inequalities where the parameter variations of the two oscillators and their differences are modeled by polytopic matrices. The theoretical result is successfully applied to an array of transistor-based oscillators used in “smart antenna” systems.     

Exponential synchronization of switched genetic oscillators with time-varying delays

This paper addresses the problem of exponential synchronization of switched genetic oscillators with time-varying delays. Switching parameters and three types of nonidentical time-varying delays, that is, the self-delay, the intercellular coupling delay, and the regulatory delay are taken into consideration in genetic oscillators. By utilizing the Kronecker product techniques and ‘delay-partition’ approach, a new Lyapunov–Krasovskii functional is proposed. Then, based on the average dwell time approach, Jensen?s integral inequality, and free-weighting matrix method, delay-dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs). These conditions guarantee the exponential synchronization of switched genetic oscillators with time-varying delays whose upper bounds of derivatives are known and unknown, respectively. A numerical example is presented to demonstrate the effectiveness of our results.     

Event-triggered synchronization control of complex networks with adaptive coupling strength

The event-triggered synchronization control problem is concerned for a class of complex networks with nonlinearly coupling function and adaptive coupling strength. Given a state-based event-trigger mechanism and the threshold, an event-triggered control method is introduced to make complex networks achieve exponential synchronization. By combining the Lyapunov stability theory and the knowledge of graph theory, a sufficient condition is established such that complex networks can achieve exponential synchronization. Then, the feasibility of the event-triggered control is analyzed. Moreover, the second-order Kuramoto oscillators is taken into account. And the event-triggered control strategy is used to make the oscillators achieve exponential synchronization. Meanwhile, two simulation results about the second-order Kuramoto oscillators are given to show the effectiveness of results.     

Biological applications of the “Filtered” Van der Pol oscillator

The present article deals with the development of an oscillatory model, which generates waveforms corresponding to ECG patterns. The present oscillatory system relies on coupling of oscillators derived from the famous VDP oscillator. We demonstrate that inducing a relaxation type of dynamics in the models contributes to their successful generation of ECG like signals. Furthermore, an interesting affinity is found, which associates the present models with a version of the well-known practical Wien Bridge oscillator. The presently discussed system relies on coupled elementary oscillator units. The present coupling is due to merely two units. The model, however, is likely to become even more realistic by coupling in the same manner an assembly of relatively many oscillators.     

Bounded controls for discrete-time linear systems subject to input time delay

This paper investigates the global stabilization of discrete-time linear systems with input time delay by bounded controls. Based on some special canonical forms containing time delays both in its input and state, two special discrete-time linear systems---multiple integrators and oscillators are first considered. The global stabilizing controllers are respectively established, and moreover, explicit conditions are established to guarantee the stability of the closed-loop systems. Subsequently, a concise design method is proposed for globally stabilizing general discrete-time linear system by combining the design methods for multiple integrators and oscillators. The designed controller is in the explicit form with explicit stability conditions being given, and thus is easier to use than the existing results. Finally, numerical simulations illustrate the effectiveness of the proposed approaches.     

双运放有源R正弦波振荡器

提出了一种振荡电路的传递函数模式，根据该函数模式设计出有源Ｒ正弦波振荡器，并给出实验结果。     

A unified approach to the realization of canonic RC-active,single as well as variable,frequency oscillators using operational amplifiers

A general, unified and systematic approach is employed to study realization of operational amplifier (OA) based sinusoidal RC-active oscillators. Both single frequency and variable frequency operations are investigated. A set of circuits is found for each case. The sets consist of 12 and 16 circuits respectively. The circuits are canonic, that is, they require the minimum number of active and passive components. For each circuit, the single frequency set requires one OA, two capacitors and four resistors, while the variable frequency set needs one OA, two capacitors and five resistors. Both sets are shown to be complete in that generation of any additional canonic circuit is not possible. Variable frequency oscillators are all single resistor controlled. They are classified into four groups according to the nature of their dependence on the variable resistor. All the circuits are laboratory tested. Experimental results agree closely with the theoretical analysis. Representative test results are included.     

Adaptive synchronization of coupled harmonic oscillators under switching topology

This paper investigates the adaptive synchronization for coupled harmonic oscillators with switching topology. Edge-based adaptive control protocols are proposed for both leaderless and leader-following synchronization for coupled harmonic oscillators with switching topology. Using Lyapunov stability theory, by parting the topology graph into connected components (containing at least two connected vertices) and isolated vertex components (containing a isolated vertex), full distributed adaptive synchronization conditions are obtained, which can guarantee that the synchronization conditions do not require any global information except a mild connection assumption. Finally numerical simulations are presented to illustrate the theoretical findings.     

Global exponential stability for multi-group neutral delayed systems based on Razumikhin method and graph theory

This paper is concerned with the global exponential stability for an original class called coupled systems of multi-group neutral delayed differential equations (MNDDEs). By employing Razumikhin method along with graph theory, sufficient conditions are established to guarantee the global exponential stability of MNDDEs, which are in the form of Razumikhin theorem. For the convenience of use, sufficient conditions in the form of coefficients are also obtained. Furthermore, coefficient-type criterion is employed to study the stability of coupled neutral delay oscillators which shows the applicability of our findings. Finally, two numerical examples are given to demonstrate the validity and feasibility of the theoretical results.     

Synthesizing antipodal chaotic waveforms

Chaotic waveforms are natural information carriers since a correspondence can be established between the symbolic dynamics of a chaotic oscillator and the symbols of a message. Message symbols can be efficiently encoded in a chaotic waveform by applying vanishingly small perturbations to an oscillator to guide its symbolic dynamics to follow a desired course. Recently, two chaotic hybrid dynamical systems were shown to have matched filters enabling robust reception of chaotic communication waveforms in the presence of noise. The first of these, the exact shift oscillator, produces waveforms with desirable properties similar to antipodal signaling, but a physical implementation may be difficult to control using small perturbations. The second oscillator, the exact folded-band oscillator, produces less optimal waveforms but is more easily controlled. Here we introduce a method for generating waveforms of the exact shift oscillator by summing waveforms from a bank of easily controlled exact folded-band oscillators. We show that any solution of the exact shift oscillator can be so constructed using only three folded-band oscillators. Thus, this scheme allows us to realize the advantages of both chaotic systems while overcoming their individual disadvantages, thereby enabling practical chaos communications.     

Secure chaotic communication based on extreme multistability

Extreme multistability is the coexistence of a large number of attractors which can be reached by varying initial conditions. In this paper we show how this fascinating phenomenon can be used for secure communication. The main advantage of the communication system based on extreme multistability over a conventional chaos-based communication system is its exceptionally high security. The proposed system consists of two identical six-order oscillators; one in the transmitter and another one in the receiver, each exhibiting the coexistence of a large number of chaotic attractors. The oscillators are synchronized using a private channel through one of the system variables, while the information is transmitted via a public channel through another variable. The information is encrypted by varying the initial condition of one of the state variables in the transmitter using a chaotic map, adhering message packages in a staggered form to the coexisting attractors within the same time series of another state variable, which leads to switching among the coexisting chaotic attractors. To ensure communication security, the duration of the packages is shorter than synchronization time, so that synchronization attacks are ineffective.     

Synchronized stationary distribution of hybrid stochastic coupled systems with applications to coupled oscillators and a Chua’s circuits network

In this paper, the existence of synchronized stationary distribution for hybrid stochastic coupled systems (HSCSs) (here, also known as stochastic coupled systems with Markovian switching) is concerned. By the existence theory of stationary distribution as well as Lyapunov method and graph theory, two kinds of sufficient criteria are presented to promise the existence of synchronized stationary distribution for HSCSs. Our results exhibit that the existence region of synchronized stationary distribution has a close relationship with the intensity of stochastic perturbation. And when stochastic perturbation vanishes, synchronized stationary distribution will become complete synchronization. Then the proposed theoretical results are successfully applied to stochastic coupled oscillators and a Chua’s circuits network. Some existence criteria of synchronized stationary distribution are also obtained. The corresponding numerical simulations are carried out to verify the validity of the theoretical results.     

An Unorthodox Paradigm of a Relaxational Self-oscillator and Some Classes of Nonlinear One-ports

The design of components with a pregiven nonlinear current-voltage characteristic is presented. On this basis, hardware realization of self-oscillators capable of functioning in different periodical regimes, without change of internal parameters, is described along with analysis of these new types of oscillators. A new aspect of connections between quasilinear and relaxational oscillations is considered with concrete examples.     

A combined time and frequency domain method for model reduction of discrete systems

A new combined time and frequency domain method for the model reduction of discrete systems in z-transfer function is presented. First, the z-transfer functions are transformed into the w-domain by the bilinear transformation, z = (1+w)/(1?w). Then, four model reduction methods—Routh approximation, Hurwitz polynomial approxima- tion, stability equation, and retaining dominant poles—are used respectively to reduce the order of the denominator polynomials in the w-domain. Least squares estimate is then used to find the optimal coefficients in the numerator polynomials of the reduced models so that the unit step response errors are reduced to a minimum. The advantages of the proposed method are that both frequency domain and time domain characteristics of the original systems can be preserved in the reduced models, and the reduced models are always stable provided the original models are stable.     

Exponential synchronization for coupled complex networks with time-varying delays and stochastic perturbations via impulsive control

This paper is concerned with the problem of exponential synchronization of coupled complex networks with time-varying delays and stochastic perturbations (CCNTDSP). Different from previous works, both the internal time-varying delay and the coupling time-varying delay are taken into account in the network model. Meanwhile, an impulsive controller is designed to realize exponential synchronization in mean square of CCNTDSP. Combining the Lyapunov method with Kirchhoff’s Matrix Tree Theorem, some sufficient criteria are obtained to guarantee exponential synchronization in mean square of CCNTDSP. Furthermore, we apply the theoretical results to study exponential synchronization of stochastic coupled oscillators with the internal time-varying delay and the coupling time-varying delay. And a synchronization criterion is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness and feasibility of our theoretical results and the superiority of impulsive control.     

Reduction of Transfer Functions by the Stability-Equation Method

A method of model reduction for reducing a high-order transfer function to its low-order models is introduced based upon the stability-equation method. The transfer functions of reduced orders are obtained directly from the pole-zero patterns of the stability-equations of the original transfer function. Comparisons with methods in the current literature are made. Extension of the proposed method to discrete systems is given.     

知识供应链视角下的企业许可关系模式研究

知识产权资产是企业的战略性资源,而许可交易是企业间知识合作的重要方式之一。本文从知识供应链的视角,研究了许可关系的五种典型交易模式,并分析各种模式的特点与适合企业,为企业制定许可战略和保持竞争优势提供依据。     

Intermittent control to stationary distribution and exponential stability for hybrid multi-stochastic-weight coupled networks based on aperiodicity

In this paper, the issue about the stationary distribution for hybrid multi-stochastic-weight coupled networks (HMSWCN) via aperiodically intermittent control is investigated. Specially, when stochastic disturbance gets to zero, the exponential stability in pth moment for hybrid multi-weight coupled networks (HMWCN) is considered. Under the framework of the Lyapunov method, M-matrix and Kirchhoff’s Matrix Tree Theorem in the graph theory, several sufficient conditions are derived to guarantee the existence of a stationary distribution and exponential stability. Different from previous work, the existing area of a stationary distribution is not only related to the topological structure of coupled networks, but also aperiodically intermittent control (the rate of control width and control duration). Subsequently, as an application to theoretical results, a class of hybrid multi-stochastic-weight coupled oscillators is studied. Ultimately, numerical examples are carried out to demonstrate the effectiveness of theoretical results and effects of the control schemes.     

Synchronization of biological neural network systems with stochastic perturbations and time delays

With advances in biochemistry, molecular biology, and neurochemistry there has been impressive progress in the understanding of the molecular properties of anesthetic agents. However, despite these advances, we still do not understand how anesthetic agents affect the properties of neurons that translate into the induction of general anesthesia at the macroscopic level. There is extensive experimental verification that collections of neurons may function as oscillators and the synchronization of oscillators may play a key role in the transmission of information within the central nervous system. This may be particularly relevant to understand the mechanism of action for general anesthesia. In this paper, we develop a stochastic synaptic drive firing rate model for an excitatory and inhibitory cortical neuronal network in the face of system time delays and stochastic input disturbances. In addition, we provide sufficient conditions for global asymptotic and exponential mean-square synchronization for this model.