در این مقاله یک سیستم فوق آشوبی جدید پیچیده با رفتارهای جذاب معرفی خواهیم نمود. ما تجزیه‌وتحلیل‌های استاندارد سیستم‌های فوق آشوبی ازجمله نمودار دوشاخگی، نقاط تعادل، نقشه پوانکاره، بعد کاپلان-یورک و نماهای لیاپانوف را انجام خواهیم داد. از خصوصیات سیستم‌های فوق آشوبی می‌توان به پیچیدگی بالاتر، مقاومت پارامتری بیشتر و حساسیت به تغییرات بسیار کوچک در شرایط اولیه اشاره کرد. در ادامه ثابت خواهیم نمود که سیستم معرفی‌شده بسیار پیچیده‌تر از سیستم‌های فوق آشوبی مشابه است که می‌تواند برای استفاده در رمزگذاری و پنهان‌سازی داده‌ها بسیار ارزشمند باشد. در مرحله بعدی، یک کنترل‌کننده مودلغزشی سریع برای همزمان سازی زمان محدود سیستم فوق آشوبی معرفی خواهیم نمود و پایداری کنترل‌کننده جدید را ثابت خواهیم کرد. نشان خواهیم داد با اعمال اغتشاش و نامعینی به سیستم، هر دو مرحله کنترل مودلغزشی دارای ویژگی‌های همگرایی زمان محدود هستند. سرانجام، مقایسه‌ای بین کنترل‌کننده جدید طراحی‌شده با کنترل‌کننده مشابه ازلحاظ زمان همگرایی انجام خواهد شد. در پایان، نتایج با استفاده از نرم‌افزار متلب شبیه‌سازی و اثبات‌شده‌اند. نتایج نشان می‌دهد سیستم فوق آشوبی جدید با جاذب‌های فراوان بسیار پیچیده‌تر از سیستم‌های مشابه بوده و کنترل‌کننده پیشنهادی نیز پاسخ همگرایی سریع‌تری را نسبت به کنترل‌کننده مشابه، دارا است. Manuscript profile

This paper constructs a new 6–D hyper–chaotic system with complex dynamic behaviors for se-cure communication scheme. We analyze the chaotic attractor, bifurcation diagram, equilibrium points, Poincare map, Lyapunov exponent behaviors, and Control parameter. The more nonlinear the autonomous system is and the higher the parametric sensitivity it is, the more performative it will be and the more difficult it will be to decode. We will show that the designed system will have attractive and different behaviors due to very small changes in control parameters, which is a sign of the high sensitivity of the system. Then, with the construction of master-slave systems and the design of a new terminal sliding mode controller, the application of the hyper-chaotic system in synchronization and transmission of secure communications is shown. Finally, using the MATLAB simulation, the results are confirmed for the new hyper–chaotic system Manuscript profile

In this paper, a new adaptive controller based on barrier function is designed for high-order nonlinear systems with a sum of the uncertainty. Accordingly, in this paper, a sliding mode controller is used, which can create asymptotic convergence and at the same time can deal with disturbances. The main drawbacks of sliding mode control can be considered as asymptotic convergence, chattering phenomenon, stimulus saturation, adaptive gain estimation and failure to deal with oscillating uncertainties. In this paper, the sliding mode control is used to deal with the phenomenon of asymptotic convergence and chattering and the barrier function is used to overcome the uncertainties of interest and fluctuation. The advantages of the proposed method include elimination of the chatting phenomenon, convergence in finite-time, compatibility with time-varying uncertainties, no use of estimation and no need for high information of disturbances. Stability analysis showed that under the proposed controller the tracking errors approach the convergence region close to zero and provide faster convergence. Finally, to prove the efficiency of the controller, based on hyperchaotic synchronization, we apply the proposed controller to the new 5D hyperchaotic system. The results showed that the proposed controller, despite the disturbances applied to the system, provides fast convergence and eliminates the chatting phenomenon. Manuscript profile

This paper constructs a novel 4D system with nonlinear complex dynamic behaviors. By analyzing the hyperchaotic attractors, bifurcation diagram, equilibrium points, Poincare map, Kaplan–Yorke dimension, and Lyapunov exponent behaviors, we prove that the introduced system has complex and nonlinear behavior. Next, the work describes a finite-time terminal sliding mode controller scheme for the synchronization and stability of the novel hyperchaotic system. All the results obtained from the proposed control are verified using Lyapunov stability theory. For synchronization, both systems designed with different parameters and model uncertainties are disturbed. Both stages of the finite-time terminal sliding mode controller have been shown to have fast convergence properties. Simply put, it has been shown that the state paths of both master and slave systems can reach each other in a finite–time. The new controller feature is that the terminal sliding surface designed with a high–order power function of error and derivative of error, is stable in finite–time. At last, using the MATLAB simulation, the results are confirmed for the new hyperchaotic system Manuscript profile