Research Topics

Controlling Chaos

  Delayed feedback control schema

• Stabilizing unstable steady states, periodic and aperiodic orbits of dynamical systems.

• Delayed feedback control: Theory and application to various dynamical systems.

• Systems with time delay in general.

    Dynamics of publications in the field of chaos control

Synchronization

Antiphase synchronization of two clocks (firstly discovered by Huygens in 1665)

• Synchronization of chaotic systems. Generalized synchronization. Weak and strong synchronization of chaos. 

• Using chaos synchronization for secure communications.

• Synchronization of time-delayed systems.

Dynamics of publications in the field of chaos synchronization

Time series analysis

• Algorithms for estimating Lyapunov exponents and dimension of a strange attractor from a chaotic time series. 

• Estimating conditional Lyapunov exponents from two time series taken from drive and response systems. 

Excitable systems

Simple example of excitable system 

• Controlling spatio-temporal chaos in excitable systems with an application to the cardiology. 

• Beat phenomenon in excitable systems and parasistolic arrhythmia.   

Spiral wave in a model of dog's heart