13 research outputs found
Lag synchronization and scaling of chaotic attractor in coupled system
We report a design of delay coupling for lag synchronization in two
unidirectionally coupled chaotic oscillators. A delay term is introduced in the
definition of the coupling to target any desired lag between the driver and the
response. The stability of the lag synchronization is ensured by using the
Hurwitz matrix stability. We are able to scale up or down the size of a driver
attractor at a response system in presence of a lag. This allows compensating
the attenuation of the amplitude of a signal during transmission through a
delay line. The delay coupling is illustrated with numerical examples of 3D
systems, the Hindmarsh-Rose neuron model, the R\"ossler system and a Sprott
system and, a 4D system. We implemented the coupling in electronic circuit to
realize any desired lag synchronization in chaotic oscillators and scaling of
attractors.Comment: 10 pages, 7 figure
Complex Dynamics in Physiological Systems: From Heart to Brain
Nonlinear dynamics has become an important field of research in recent years in many areas of the natural sciences. In particular, it has potential applications in biology and medicine; nonlinear data analysis has helped to detect the progress of cardiac disease, physiological disorders, for example episodes of epilepsy, and others. This book focuses on the current trends of research concerning the prediction of sudden cardiac death and the onset of epileptic seizures, using the nonlinear analysis based on ECG and EEG data. Topics covered include the analysis of cardiac models and neural models. The book is a collection of recent research papers by leading physicists, mathematicians, cardiologists and neurobiologists who are actively involved in using the concepts of nonlinear dynamics to explore the functional behaviours of heart and brain under normal and pathological conditions. This collection is intended for students in physics, mathematics and medical sciences, and researchers in interdisciplinary areas of physics and biology
Design of Coupling for Synchronization of Chaotic Oscillators
A general procedure is discussed to formulate a coupling function capable of targeting desired responses
such as synchronization, antisynchronization, and amplitude death in identical as well as mismatched chaotic
oscillators. The coupling function is derived for unidirectional, mutual, and matrix type coupling. The matrix
coupling, particularly, is able to induce synchronization, antisynchronization, and amplitude death simultaneously
in different state variables of a response system. The applicability of the coupling is demonstrated in
spiking-bursting Hindmarsh-Rose neuron model, Rössler oscillator, Lorenz system, Sprott system, and a
double scroll system. We also report a scaling law that defines a process of transition to synchronization