High performance computing: ·Development and implementation of novel algorithms to solve partial differential equations in two- and three-dimensional regular and irregular domains. ·Computer modeling of complex systems using supercomputers, as well as graphics cards (GPUs). ·Simulations and large data visualization of complex systems in or near-real time locally or over the web. Experiments in complex systems: ·Cardiac dynamics.Study the voltage and calcium dynamics of cardiac tissue using heart sections or whole hearts from fish and mice to large mamals horses. Using voltage- and calcium-sensitive dyes and ultrafast cameras, we record the dynamics of voltage and calcium waves and study their instabilities associated with arrhythmias. ·Dynamics of spiral and scroll waves. ·Mechanisms of bifurcation and period-doublings in time and in space. ·Methods for chaos control and synchronization. ·Chemical, physical, and other biophysical oscillators with complex dynamics and instabilities. Examples: spiral and scroll waves in the Belousov–Zhabotinsky reaction, saline oscillator. Mathematical modeling of complex systems: ·Development and analysis of mathematical models that describe generic or detailed dynamics of excitable and oscillatory media (heart, neurons, chemical reactions, calcium signaling, physical and biological oscillators, etc.). ·Study of bifurcations and chaotic (organized and disorganized) dynamics of excitable and oscillatory systems. ·Develop and apply control methods for suppressing or synchronizing complex dynamics. ·Study of stability and instabilities of spiral waves and three-dimensional scroll waves in idealized and realistic domains of excitable media. In most projects there is crossover between theory, simulations and experiments, where experiments (simulations) are used to guide theory and simulations (experiments).