Chaos synchronization in a 6-D hyperchaotic system with self-excited attractor

This paper presented stability application for chaos synchronization using a 6-D hyperchaotic system of different controllers and two tools: Lyapunov stability theory and Linearization methods. Synchronization methods based on nonlinear control strategy is used. The selecting controller's methods have been modified by applying complete synchronization. The Linearization methods can achieve convergence according to the of complete synchronization. Numerical simulations are carried out by using MATLAB to validate the effectiveness of the analytical technique

Strategies of linear feedback control and its classification

This paper is concerned with the control problem for a class of nonlinear dynamical (hyperchaotic) systems based on linear feedback control strategies. Since the obtaining positive feedback coefficients are required for these strategies. From this point of view, the available ordinary/dislocated/enhancing and speed feedback control strategies can be classified into two main aspects: control the dynamical systems or can't be control although it own a positive feedback coefficients. So, we focused on these cases, and suggest a new method to recognize which system can be controller it or not. In this method, we divided the positive feedback coefficient which obtain from these strategies in to four categories according to possibility of suppression and show the reason for each case. Finally, numerical simulations are given to illustrate and verify the results

An optimal control for complete synchronization of 4D Rabinovich hyperchaotic systems

This paper derives new results for the complete synchronization of 4D identical Rabinovich hyperchaotic systems by using two strategies: active and nonlinear control. Nonlinear control strategy is considered as one of the powerful tool for controlling the dynamical systems. The stabilization results of error dynamics systems are established based on Lyapunov second method. Control is designed via the relevant variables of drive and response systems. In comparison with previous strategies, the current controller (nonlinear control) focuses on convergence speed and the minimum limits of relevant variables. Better performance is to achieve full synchronization by designing the control with fewer terms. The proposed control has certain significance for reducing the time and complexity for strategy implementation

Projective and hybrid projective synchronization of 4-D hyperchaotic system via nonlinear controller strategy

Nonlinear control strategy was established to realize the Projective Synchronization (PS) and Hybrid Projective Synchronization (HPS) for 4-D hyperchaotic system at different scaling matrices. This strategy, which is able to achieve projective and hybrid projective synchronization by more precise and adaptable method to provide a novel control scheme. On First stage, three scaling matrices were given in order to achieving various projective synchronization phenomena. While the HPS was implemented at specific scaling matrix in the second stage.  Ultimately, the precision of controllers were compared and analyzed theoretically and numerically. The long-range precision of the proposed controllers are confirmed by third stage

A New Simple 6D Hyperchaotic System with Hyperbolic Equilibrium and Its Electronic Circuit

This paper represents a sequential design of controlling from a 3D chaotic system to a simple 6D hyperchaotic system by adding three linear controllers via state feedback control and coupling strategies. The new 6D system has a unique non-hyperbolic equilibrium point with four positive Lyapunov exponents (LE). Moreover, some dynamic properties are analyzed which inclined equilibrium and their stability, dissipative, conservative, and multistability. In addition, the corresponding analog electronic circuit is designed and implemented to verify the new simple 6D hyperchaotic system. Finally, the NI Multisim simulation results observed from the digital oscilloscope are consistent with the mathematical simulation based on the Matlab R2021a

Coexisting of self-excited and hidden attractors in a new 4D hyperchaotic Sprott-S system with a single equilibrium point

Coexisting self-excited and hidden attractors for the same set of parameters in dissipative dynamical systems are more interesting, important, and difficult compared to other classes of hidden attractors. By utilizing of nonlinear state feedback controller on the popular Sprott-S system to construct a new, unusual 4D system with only one nontrivial equilibrium point and two control parameters. These parameters affect system behavior and transformation from hidden attractors to self-excited attractors or vice versa. As compared to traditional similar kinds of systems with hidden attractors, this system is distinguished considering it has (-2) positive Lyapunov exponents with maximal Lyapunov exponent. In addition, the coexistence of multi-attractors and chaotic with 2-torus are found in the system through analytical results and experimental simulations which include equilibrium points, stability, phase portraits, and Lyapunov spectrum. Furthermore, the anti-synchronization realization of two identical new systems is done relying on Lyapunov stability theory and nonlinear controllers strategy. lastly, the numerical simulation confirmed the validity of the theoretical results

Chaos synchronization of nonlinear dynamical systems via a novel analytical approach

This paper deals with the synchronization between two non-identical 4-D hyperchaotic systems. The nonlinear control technique is used for synchronization. The stability analysis of the error dynamics system is done by (i) Lyapunov's second method and (ii) Cardano's method. Four different expressions of the controller are presented in the paper and a comparison between the two methods are given. We notice that the Cardano's method is better than the Lyapunov approach. Finally, theoretical and numerical simulations are given to illustrate and verify the results. Keywords: Complete synchronization, Modified hyperchaotic Pan system, Hyperchaotic Liu system, Lyapunov's second method, Cardano's method, Nonlinear control strateg

Dynamical Analysis and Adaptive Finite-Time Sliding Mode Control Approach of the Financial Fractional-Order Chaotic System

In this work, we studied the complex behaviors of the fractional-order financial chaotic system, consisting of a simple, relatively chaotic system with two quadratic nonlinearities (QN) and a sextic nonlinearity (SN). We completed and enriched the results presented in the study of Subartini et al. (2021). As a result of this, our study focused more on the fractional order and adaptive finite-time sliding mode control in the financial risk chaotic system. The dynamical behaviors of the financial chaotic system (FCS) with two QN and an SN were analyzed, and the stability was investigated via the Cardano method. The stability analysis showed that the real part of all the roots was negative, which confirmed the stability of the new system under the typical parameters. By using the MATLAB simulation, these properties were characterized, including the phase portraits, 0-1 test, Poincaré map, bifurcation diagram, and Lyapunov exponent. The analysis showed that the financial risk chaotic system of fractional order was able to exhibit chaotic behavior and periodical behavior. In spite of external perturbations and uncertainty, an adaptive finite-time sliding mode control strategy was devised to guide the states of the financial chaotic system to the origin in a finite amount of time. MATLAB phase plots were employed in this study to illustrate all the main results

SARS-CoV-2 vaccination modelling for safe surgery to save lives: data from an international prospective cohort study

Background: Preoperative SARS-CoV-2 vaccination could support safer elective surgery. Vaccine numbers are limited so this study aimed to inform their prioritization by modelling. Methods: The primary outcome was the number needed to vaccinate (NNV) to prevent one COVID-19-related death in 1 year. NNVs were based on postoperative SARS-CoV-2 rates and mortality in an international cohort study (surgical patients), and community SARS-CoV-2 incidence and case fatality data (general population). NNV estimates were stratified by age (18-49, 50-69, 70 or more years) and type of surgery. Best- and worst-case scenarios were used to describe uncertainty. Results: NNVs were more favourable in surgical patients than the general population. The most favourable NNVs were in patients aged 70 years or more needing cancer surgery (351; best case 196, worst case 816) or non-cancer surgery (733; best case 407, worst case 1664). Both exceeded the NNV in the general population (1840; best case 1196, worst case 3066). NNVs for surgical patients remained favourable at a range of SARS-CoV-2 incidence rates in sensitivity analysis modelling. Globally, prioritizing preoperative vaccination of patients needing elective surgery ahead of the general population could prevent an additional 58 687 (best case 115 007, worst case 20 177) COVID-19-related deaths in 1 year. Conclusion: As global roll out of SARS-CoV-2 vaccination proceeds, patients needing elective surgery should be prioritized ahead of the general population