Narrow Results

Coupled chaotic oscillators are found to be able to achieve the partial synchronization state in some networks. The scaling relation between the synchronization time and the coupling at the synchronous threshold is found and explained. In the studies, it was found that the coupling of the synchronization properties of networks is not homogeneous.

This paper presents a chaotic oscillator based on the nonlinearity of the typical transconductance (G_m). This chaotic circuit only consists of 13 MOS transistors and three grounded capacitors, which is one of the smallest chaotic oscillators. This circuit operates on low voltage supply (± 1.5 V). The dimensionless form of the circuit is also introduced to confirm the circuit simulation.

A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel filter is described. The Bessel unit plays the role of "three-in-one": a delay line, an amplifier and a filter. Results of hardware experiments and numerical simulation are presented. Depending on the parameters of the nonlinear unit the oscillator operates either in a one-scroll or two-scroll mode. Two positive Lyapunov exponents, found at larger values of the negative slopes of the nonlinear function, characterize the oscillations as hyperchaotic.

An electronic circuit realization of a modified Lorenz system, which is multiplier-free, is described. The well-known butterfly chaotic attractor is experimentally observed verifying that the proposed modified system does capture the essential dynamics of the original Lorenz system. Furthermore, we clarify that the butterfly attractor is a compound structure obtained by merging together two simple attractors after performing one mirror operation.

A numerical study of the dynamics of two mutually coupled nonlinear oscillators, at least one of them being in a chaotic state, is presented. Each of these oscillators is described as a three-dimensional autonomous flux. The phase of the oscillations, the Lyapunov spectrum and the bifurcation diagram are studied as functions of the coupling strength. When this is increased the two systems entrain, starting to oscillate in phase; then, for further increase, chaos suppression occurs. The study of different cases shows a rich phenomenology which includes multistability, and several bifurcation phenomena. The transitions to chaos suppression and phase synchronization are studied and interpreted in Fourier space on the base of a simple mechanism of mutual induction of motions by means of the coupling.

We propose a simple continuous-time system for chaos generation based on a third-order abstract canonical mathematical model. Nonlinearity in this model is introduced by a bipolar switching constant, which reflects the behavior of a digital inverter. A simple area efficient implementation of the system in a 1.2 μ CMOS process is presented. Experimental results from a tested chip are shown.

A novel system of nonlinear differential equations is proposed. This system is capable of generating a complex four-wing butterfly chaotic attractor by relying on two embedded state-controlled binary switches. Hence, the system is fully autonomous and does not require external forcing to create this attractor. Furthermore, digital logic operations (e.g. AND/OR) performed on the outputs of the two switches are permitted and effectively alter the dynamics of the system. Our findings are validated via experimental results.

A control scheme is applied between two different oscillators to study their phase synchronization. It utilizes unidirectional signal coupling and only measures the time interval when the trajectories to the two oscillators' attractors cross the Poincaré surfaces respectively. By using this scheme, phase synchronization (without 2π phase slips) can be obtained between two different chaotic systems whose signal variables have large amplitude mismatch. This unidirectional signal coupling also provides a minimum information flow from the driving system to the response system. Therefore it can be used in synchronizing systems with substantially different dynamics via a channel with low information rate.

In this paper we study the relationships between local and global properties in networks of dynamical systems by focusing on two global properties, synchronization and peak-to-peak dynamics, and on two local properties, coherence of the components of the network and coupling strength. The analysis is restricted to networks of low-dimensional chaotic oscillators, i.e. oscillators which have peak-to-peak dynamics when they work in isolation. The results are obtained through simulation, first by considering pairs of coupled Lorenz, Rössler and Chua systems, and then by studying the behavior of spatially extended tritrophic food chains described by the Rosenzweig–MacArthur model. The conclusion is that synchronization and peak-to-peak dynamics are different aspects of the same collective behavior, which is easily obtained by enhancing local coupling and coherence. The importance of these findings is briefly discussed within the context of ecological modeling.

A system for generating a multi-butterfly chaotic attractor using the multi-level-logic pulse-excitation technique is proposed. Two-butterfly, three-butterfly and four-butterfly attractors are demonstrated. Results from an experimental setup are also shown.

This paper reviews pulse-excitation as a technique for inducing chaos and provides a review of circuits that have been designed based on this technique. A clock-driven chaotic van der Pol oscillator is also presented. Vulnerability of this class of chaos generators to power supply attacks is demonstrated.

In this paper, by modifying a known two-dimensional oscillator, we obtain an interesting new oscillator with coexisting limit cycles and point attractors. Then by changing this new system to its forced version and choosing a proper set of parameters, we introduce a chaotic system with some very interesting features. In this system, not only can we see the coexistence of different types of attractors, but also a fascinating phenomenon: some initial conditions can escape from the gravity of nearby attractors and travel far away before being trapped in an attractor beyond the usual access.

In this paper, a new two-dimensional nonlinear oscillator with an unusual sequence of rational and irrational parameters is introduced. This oscillator has endless coexisting limit cycles, which make it a megastable dynamical system. By periodically forcing this system, a new system is designed which is capable of exhibiting an infinite number of coexisting asymmetric torus and strange attractors. This system is implemented by an analog circuit, and its Hamiltonian energy is calculated.

Recently, chaotic systems with hidden attractors and multistability have been of great interest in the field of chaos and nonlinear dynamics. Two special categories of systems with multistability are systems with extreme multistability and systems with megastability. In this paper, the simplest (yet) megastable chaotic oscillator is designed and introduced. Dynamical properties of this new system are completely investigated through tools like bifurcation diagram, Lyapunov exponents, and basin of attraction. It is shown that between its countable infinite coexisting attractors, only one is self-excited and the rest are hidden.

Weak signal detection is an important topic, which has been widely studied in various fields. Different from other signal processing methods, stochastic resonance (SR) can utilize noise to enhance the characteristic frequency. Inspired by the unique advantage of SR, the strongly coupled Duffing and Van der pol SR system (SCD-VSR) is investigated. The simulation results show that the relationship between the output average signal–noise ratio increase (MSNRI) and different jump values of trichotomous noise presents different odd symmetrical distribution. It is also found that a double SR phenomenon could be observed when the damping coefficient of Van der pol system is small. Moreover, as the damping coefficient of the Duffing system increases, the output response would become gradually smooth. In addition,a smaller damping force coupling coefficient combined with a large restoring force coupling coefficient would achieve better system response. In the case of detecting an analog signal, MSNRI of SCD-VSR is larger than that of both classical bistable SR system (CBSR) and coupled Duffing SR system (CDSR). In addition, the experiments suggest that SCD-VSR could obtain a higher MSNRI and better detection effect, which implies the performance is superior to CBSR and CDSR.

Prediction of dominant frequencies of two examples of current-feedback op amp (CFOA)-based Sprott's chaotic oscillators is presented through the use of simple Fourier analysis. In addition, two examples of CFOA-based Sprott's sinusoidal oscillators exhibiting periodic sinusoids are also demonstrated. In the Sprott's sinusoidal oscillators, the fundamental frequencies may be approximated by the prediction of the dominant frequencies.