Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators

In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use numerical and analytical as well as analogue simulation methods to study these systems. Then we point out how controlling of chaotic motions can be effected by algorithmic procedures requiring minimal perturbations. Finally we briefly discuss how synchronization of identically evolving chaotic systems can be achieved and how they can be used in secure communications.Comment: 31 pages (24 figures) LaTeX. To appear Springer Lecture Notes in Physics Please Lakshmanan for figures (e-mail: [email protected]

Experimental Evidence of Chaotic Resonance in Semiconductor Laser

تم في هذا البحث تقديم دراسة تجريبية بشأن إشارة الرنين في ليزر أشباه الموصلات الشواشي. تعتبر اضطرابات الرنين فعالة في تسخير مؤشرات التذبذب غير الخطية لتطبيقات مختلفة مثل إحداث الشواش والسيطرة على الشواش. تم الحصول على نتائج مثيرة للاهتمام فيما يتعلق بتأثير الرنين الشواشي عن طريق إضافة التردد على الأنظمة. يغير التردد القسري النظام الديناميكي غير الخطي من خلال قيمة حرجة ، وهناك انتقال من جاذب دوري إلى جاذب غريب. كما ان السعة لها تأثير وثيق الصلة للغاية بالنظام ، مما أدى إلى استجابة الرنين الأمثل للقيم المناسبة المتعلقة بزمن الارتباط. فيصبح النظام الشواشي منتظمًا تحت ترددات أو سعات معتدلة. كما تم تحليل هذه الديناميكيات لمخرجات الليزر من خلال السلاسل الزمنية واطياف القدرة المستخرجة (FFT) وقد تعززت بواسطة مخطط التشعب.In this paper, an experimental study has been conducted regarding the indication of resonance in chaotic semiconductor laser.  Resonant perturbations are effective for harnessing nonlinear oscillators for various applications such as inducing chaos and controlling chaos. Interesting results have been obtained regarding to the effect of the   chaotic resonance by adding the frequency on the systems. The frequency changes nonlinear dynamical system through a critical value, there is a transition from a periodic attractor to a strange attractor. The amplitude has a very relevant impact on the system, resulting in an optimal resonance response for appropriate values related to correlation time. The chaotic system becomes regular under a moderate frequencies or amplitudes. These dynamics of the laser output are analyzed by time series, FFT and bifurcation diagram as a result

Stochastic and Nonlinear Dynamics in Low-Temperature Plasmas

Low-temperature (LT) plasmas have a substantial role in diverse scientific areas and modern technologies. Their stochastic and nonlinear dynamics strongly determine the efficiency and effectiveness of LT plasma-based procedures involved in applications such as etching, spectrochemical analysis, deposition of thin films on substrates, and others. Understanding and controlling complex behaviors in LT plasmas have become a serious research problem. Modeling their behavior is also a major problem. However, models based on hydrodynamic equations have proven to be useful in their study. In this chapter, we expose the use of fluid models taking into account relevant kinetic processes to describe out from equilibrium LT plasma behavior. Selected topics on the stability, stochastic, and nonlinear dynamics of LT plasmas are discussed. These include the coexistence of diffusive and wave-like particle transport and delayed feedback control of oscillatory regime with relaxation

Unreduced Complex Dynamics of Real Computer and Control Systems

8 pages, 42 eqs, 23 refs; presented at the 20th International Conference on Control Systems and Computer Science (27-29 May 2015, Bucharest, Romania), http://cscs20.acs.pub.ro/International audienceThe unreduced dynamic complexity of modern computer, production, communication and control systems has become essential and cannot be efficiently simulated any more by traditional, basically regular models. We propose the universal concept of dynamic complexity and chaoticity of any real interaction process based on the unreduced solution of the many-body problem by the generalised effective potential method. We show then how the obtained mathematically exact novelties of system behaviour can be applied to the development of qualitatively new, complex-dynamical kind of computer and control systems