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  • Belousov-Zhabotinsky Patterns

Target
Spirals

  • Design and Control of Wave Propagation Patterns in Excitable Media

T. Sakurai, E. Mihaliuk, F. Chirila, and K. Showalter, "Design and Control of Wave Propagation Patterns in Excitable Media," Science 296, 2009-2012 (2002).

Four Petal Trajectory
Wave Undergoing Random Walk
Two Waves with Mutual Interaction

  • Complex Networks 

M. R. Tinsley, J. Cui, F. V. Chirila, A. Taylor, S. Zhong, and K. Showalter, "Spatiotemporal networks in addressable excitable media," Phys. Rev. Lett. 95, 038306 (1-4) (2005).

A. J. Steele, M. Tinsley, and K. Showalter, "Spatiotemporal Dynamics of Networks of Excitable Nodes," Chaos 16, 015110-1-9 (2006).

  • Spatiotemporal Networks in Addressable Excitable Media

Experimental Static Network with 300 Links

  • Synchronization and Dynamical Quorum Sensing – Global Coupling

A. F. Taylor, M. R. Tinsley, F. Wang, Z. Huang, and K. Showalter, '' Dynamical Quorum Sensing and Synchronization in Large Populations of Chemical Oscillations," Science 323, 614-617 (2009). '' Supporting Online Material."

  • Population Density Dependent Behavior of Discrete Chemical Oscillators

Low Particle Density – High Exchange Rate
High Particle Density – High Exchange Rate
High Particle Density – Low Exchange Rate
Low Particle Density – Low Exchange Rate

  • Synchronization and Dynamical Quorum Sensing – Local Coupling

Mark R. Tinsley, Annette F. Taylor,   Zhaoyang Huang, and Kenneth Showalter, '' Emergence of Collective Behavior in Groups of Excitable Catalyst-Loaded Particles: Spatiotemporal Dynamical Quorum Sensing," Phys. Rev. Lett. 102, 158301-1-4 (2009).

  • Population Density Dependent Behavior of Discrete Chemical Oscillators

Group of Excitable Particles – Pacemaker
Group of Excitable Particles – Spirals

  • Collective Behavior in Excitable Media: Interacting Particle-Like Waves

A. J. Steele, M. R. Tinsley, and K. Showalter, ''Collective Behavior of Stabilized Reaction-Diffusion Waves," Chaos 18, 026108-1-8 (2008).

M. R. Tinsley, A. J. Steele,  and K. Showalter, ''Collective Behavior of Particle-Like Chemicle Waves," Eur. Phys. J. Special Topics 165, 161-167 (2008).

  • Collective Behavior of Particle-Like Chemical Waves

Processional Behavior: All-to-All Interactions
Processional Behavior: Pairwise Interaction
Rotational Behavior: All-to-All Interactions
Rotational Behavior: Pairwise Interactions

  • Wave Propagation Induced by Noise

S. Kádár, J. Wang, and K. Showalter, "Noise Supported Traveling Waves in Subexcitable Media," Nature 391, 770-772 (1998).

J. Wang, S. Kádár, P. Jung, and K. Showalter, "Noise Driven Avalanche Behavior in Subexcitable Media," Phys. Rev. Lett. 82, 855-888 (1999).

Noise Driven Avalanche Behavior in Subexcitable Media
Noise Supported Traveling Waves in Subexcitable Media

  • Wave Formation in Three-Dimensional Excitable Media

T. Amemiya, S. Kádár, P. Kettunen, and K. Showalter, "Spiral Wave Formation in Three-Dimensional Excitable Media," Phys. Rev. Lett. 77, 3244-3247 (1996).

Target Pattern
Spiral Pattern
Two Target Patterns
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