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A significant attention has concentrated on systems with "hidden attractors" in recent years. The aim of this work is to study an oscillator displaying "hidden attractors". The oscillator has all nonlinear terms but no equilibrium. The oscillator exhibits attractive dynamics such as chaos, bubble bifurcation, symmetrical attractors, and boosting attractors. Oscillator's feasibility is verified by a microcontroller. Utilizing the oscillator for biomedical image encryption illustrates its application. In addition, the adaptive control is designed for the oscillator. [ABSTRACT FROM AUTHOR]

[Display omitted] • This article proposes a new robust nonlinear controller that stabilizes a chaotic finance system in a finite-time without cancellation of the spacecraft's nonlinear terms, it improves the efficiency of the closed-loop. • It accomplishes an oscillation-free faster convergence of the perturbed state variables to the desired steady-state. • The proposed controller is insensitive to the parameter uncertainties of the nonlinear terms and exogenous disturbances. • The paper performs a comparative study to verify the performance and efficiency of the proposed controller. Robust, stable financial systems significantly improve the growth of an economic system. The stabilization of financial systems poses the following challenges. The state variables' trajectories (i) lie outside the basin of attraction, (ii) have high oscillations, and (iii) converge to the equilibrium state slowly. This paper aims to design a controller that develops a robust, stable financial closed-loop system to address the challenges above by (i) attracting all state variables to the origin, (ii) reducing the oscillations, and (iii) increasing the gradient of the convergence. This paper proposes a detailed mathematical analysis of the steady-state stability, dissipative characteristics, the Lyapunov exponents, bifurcation phenomena, and Poincare maps of chaotic financial dynamic systems. The proposed controller does not cancel the nonlinear terms appearing in the closed-loop. This structure is robust to the smoothly varying system parameters and improves closed-loop efficiency. Further, the controller eradicates the effects of inevitable exogenous disturbances and accomplishes a faster, oscillation-free convergence of the perturbed state variables to the desired steady-state within a finite time. The Lyapunov stability analysis proves the closed-loop global stability. The paper also discusses finite-time stability analysis and describes the controller parameters' effects on the convergence rates. Computer-based simulations endorse the theoretical findings, and the comparative study highlights the benefits. Theoretical analysis proofs and computer simulation results verify that the proposed controller compels the state trajectories, including trajectories outside the basin of attraction, to the origin within finite time without oscillations while being faster than the other controllers discussed in the comparative study section. This article proposes a novel robust, nonlinear finite-time controller for the robust stabilization of the chaotic finance model. It provides an in-depth analysis based on the Lyapunov stability theory and computer simulation results to verify the robust convergence of the state variables to the origin. [ABSTRACT FROM AUTHOR]

This paper considers the distributed consensus control of nth-order uncertain nonlinear multi-agent systems (MASs) with fuzzy dead-zone (DZ). Unlike the existing works which describes the DZ constraint by the conventional deterministic models, this work describes the DZ by the fuzzy and uncertain value. Therefore, some imposed restricting assumptions on the DZ parameters such as known bounds of the DZ slopes, or linear and deterministic model for DZ description which exist in the previous works are removed in this work. In the proposed scheme, the neural network (NN) is invoked to model the uncertain nonlinearities of the follower agents and uncertain interaction of their neighbors. To decrease the number of adaptive parameters and computational load, maximum norm of the weight coefficients of the NN is considered as an adjustable parameter and tuned online. Also, to decrease the controller complexity and eliminate the repeated derivatives of nonlinear functions in the controller, the dynamic surface control (DSC) method is used to develop the proposed distributed consensus scheme. Stability analysis based on the Lyapunov direct method guarantees that all of the signals in the closed-loop MAS are semi-globally uniformly ultimately bounded and the consensus error converges to a bound dependent on the design parameters. Therefore, appropriate choice of the design parameters makes the bound small. Simulation results on a well-known example demonstrate the effectiveness of the developed consensus algorithm. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a new secure communications approach, obtained by combining into one scheme chaotic modulation, recursive encryption and chaotic masking. The objective is achieved by designing control laws to synchronize two hyperchaotic Lorenz systems with encrypted states via a backstepping technique. The encryption process relies on a Unified chaotic system, driven by the hyperchaotic Lorenz system, as well as on a recursive encryption algorithm that exploits an n -fold composition of an invertible function. A novel theorem is proved, which assures that the transmitted message is recovered at the receiver side by virtue of the synchronization of the two Lorenz systems via backstepping design. Numerical simulations are carried out using image and text as transmitted signals, with the aim to show the effectiveness of the conceived chaos-based encryption scheme. [ABSTRACT FROM AUTHOR]

Researchers have paid significant attention on hyperjerk systems, especial hyperjerk ones with chaos. A new hyperjerk system with seven terms and two parameters is analyzed. Chaotic attractors as well as coexisting attractors are displayed by the hyperjerk system. Thus it is a new multi-stable chaotic hyperjerk system. Further properties of the proposed hyperjerk system such as circuit design and backstepping-based control and synchronization are reported. [ABSTRACT FROM AUTHOR]

In this paper, an autonomous Toda jerk oscillator is proposed and analysed. The autonomous Toda jerk oscillator is obtained by converting an autonomous two-dimensional Toda oscillator with an exponential nonlinear term to a jerk oscillator. The existence of Hopf bifurcation is established during the stability analysis of the unique equilibrium point. For a suitable choice of the parameters, the proposed autonomous Toda jerk oscillator can generate antimonotonicity, periodic oscillations, chaotic oscillations and bubbles. By introducing two additional parameters in the proposed autonomous Toda jerk oscillator, it is possible to control partially or totally the amplitude of its signals. In addition, electronic circuit realization of the proposed Toda jerk oscillator is carried out to confirm results found during numerical simulations. The commensurate fractional-order version of the proposed autonomous chaotic Toda jerk oscillator is studied using the stability theorem of fractional-order oscillators and numerical simulations. It is found that periodic oscillations and chaos exist in the fractional-order form of the proposed Toda jerk oscillator with order less than three. Finally, combination synchronization of two fractional-order proposed autonomous chaotic Toda jerk oscillators with another fractional-order proposed autonomous chaotic Toda jerk oscillator is analysed using the nonlinear feedback control method. [ABSTRACT FROM AUTHOR]

A novel 4-D chaotic hyperjerk system with four quadratic nonlinearities is presented in this work. It is interesting that the hyperjerk system has no equilibrium. A chaotic attractor is said to be a hidden attractor when its basin of attraction has no intersection with small neighborhoods of equilibrium points of the system. Thus, our new non-equilibrium hyperjerk system possesses a hidden attractor. Chaos in the system has been observed in phase portraits and verified by positive Lyapunov exponents. Adaptive backstepping controller is designed for the global chaos control of the non-equilibrium hyperjerk system with a hidden attractor. An electronic circuit for realizing the non-equilibrium hyperjerk system is also introduced, which validates the theoretical chaotic model of the hyperjerk system with a hidden chaotic attractor. [ABSTRACT FROM AUTHOR]

By analyzing the issue of chaos synchronization, it can be noticed the lack of a general approach, which would enable any type of synchronization to be achieved. Similarly, there is the lack of a unified method for synchronizing both continuous-time and discrete-time systems via a scalar signal. This paper aims to bridge all these gaps by presenting a novel general unified framework to synchronize chaotic (hyperchaotic) systems via a scalar signal. By exploiting nonlinear observer design, the approach enables any type of synchronization defined to date to be achieved for both continuous-time and discrete-time systems. Referring to discrete-time systems, the method assures any type of dead beat synchronization (i.e., exact synchronization in finite time), thus providing additional value to the conceived framework. Finally, the topic of synchronizing special type of systems, such as those characterized by the absence of equilibrium points, is also discussed. [ABSTRACT FROM AUTHOR]

Recently, systems with chaos and the absence of equilibria have received a great deal of attention. In our work, a simple five-term system and its anti-synchronization are presented. It is special that the system has a hyperbolic sine nonlinearity and no equilibrium. Such a system generates chaotic behaviours, which are verified by phase portraits, positive Lyapunov exponent as well as an electronic circuit. Moreover, the system displays multistable characteristic when changing its initial conditions. By constructing an adaptive control, chaos anti-synchronization of the system with no equilibrium is obtained and illustrated via a numerical example. [ABSTRACT FROM AUTHOR]

In this research work, a twelve-term novel 5-D hyperchaotic Lorenz system with three quadratic nonlinearities has been derived by adding a feedback control to a ten-term 4-D hyperchaotic Lorenz system (Jia, 2007) with three quadratic nonlinearities. The 4-D hyperchaotic Lorenz system (Jia, 2007) has the Lyapunov exponents L1 = 0.3684,L2 = 0.2174,L3 = 0 and L4 =−12.9513, and the Kaplan-Yorke dimension of this 4-D system is found as DKY =3.0452. The 5-D novel hyperchaotic Lorenz system proposed in this work has the Lyapunov exponents L1 = 0.4195,L2 = 0.2430,L3 = 0.0145,L4 = 0 and L5 = −13.0405, and the Kaplan-Yorke dimension of this 5-D system is found as DKY =4.0159. Thus, the novel 5-D hyperchaotic Lorenz system has a maximal Lyapunov exponent (MLE), which is greater than the maximal Lyapunov exponent (MLE) of the 4-D hyperchaotic Lorenz system. The 5-D novel hyperchaotic Lorenz system has a unique equilibrium point at the origin, which is a saddle-point and hence unstable. Next, an adaptive controller is designed to stabilize the novel 5-D hyperchaotic Lorenz system with unknown system parameters. Moreover, an adaptive controller is designed to achieve global hyperchaos synchronization of the identical novel 5-D hyperchaotic Lorenz systems with unknown system parameters. Finally, an electronic circuit realization of the novel 5-D hyperchaotic Lorenz system using SPICE is described in detail to confirm the feasibility of the theoretical model. [ABSTRACT FROM AUTHOR]

Independent, prospective, multicenter, hospital-based cross-sectional studies were conducted across 5 countries in Asia, namely, Malaysia, Vietnam, Singapore, South Korea, and the Philippines. The objectives of these studies were to evaluate the prevalence of human papillomavirus (HPV) types (high risk and others including coinfections) in women with invasive cervical cancer (ICC) and high-grade precancerous lesions.Women older than 21 years with a histologic diagnosis of ICC and cervical intraepithelial neoplasia [CIN 2 or 3 and adenocarcinoma in situ (AIS)] were enrolled. Cervical specimens were reviewed by histopathologists to confirm the presence of ICC or CIN 2/3/AIS lesion and tested with short PCR fragment10-DNA enzyme immunoassay-line probe assay for 14 oncogenic HPV types and 11 non-oncogenic HPV types. The prevalence of HPV 16, HPV 18, and other high-risk HPV types in ICC [including squamous cell carcinoma (SCC) and adenocarcinoma/adenosquamous carcinoma (ADC/ASC)] and CIN 2/3/AIS was estimated.In the 5 Asian countries, diagnosis of ICC was confirmed in 500 women [SCC (n = 392) and ADC/ASC (n = 108)], and CIN 2/3/AIS, in 411 women. Human papillomavirus DNA was detected in 93.8% to 97.0% (84.5% for the Philippines) of confirmed ICC cases [94.0%-98.7% of SCC; 87.0%-94.3% (50.0% for the Philippines) of ADC/ASC] and in 93.7% to 100.0% of CIN 2/3/AIS. The most common types observed among ICC cases were HPV 16 (36.8%-61.3%), HPV 18 (12.9%-35.4%), HPV 52 (5.4%-10.3%), and HPV 45 (1.5%-17.2%), whereas among CIN 2/3/AIS cases, HPV 16 (29.7%-46.6%) was the most commonly observed type followed by HPV 52 (17.0%-66.7%) and HPV 58 (8.6%-16.0%).This article presents the data on the HPV prevalence, HPV type distribution, and their role in cervical carcinogenesis in 5 Asian countries. These data are of relevance to public health authorities for evaluating the existing and future cervical cancer prevention strategies including HPV-DNA testing-based screening and HPV vaccination in these Asian populations. [ABSTRACT FROM AUTHOR]