West Virginia University chemists are among the first to reproduce the theoretical chimera state in a laboratory, an achievement that could lead to a better understanding of how the brain works.

The chimera of mythology is a fire-breathing beast composed of the heads of a lion, goat and snake. In the world of nonlinear dynamics, the reproduction of the chimera state, a partly synchronized, partly asynchronous system of coupled oscillators, has been as elusive to spot as the fictional Greek monster.

Professor and C. Eugene Bennett Chair in Chemistry Kenneth Showalter, in the C. Eugene Bennett Department of Chemistry at WVU and his colleague Rajarshi Roy, professor of physics and director of the Institute for Physical Science and Technology at the University of Maryland, College Park led two simultaneous experiments that reproduced the chimera state. Roy and Showalter, long-time friends working separately in two different disciplines, are the first ever to recreate the elusive theoretical chimera state in the laboratory.

“Since 2002, mathematicians and physicists have been actively investigating the chimera state because it is very unusual for a system that is partly synchronized and partly unsynchronized to be stable,” Showalter said. “We are excited to demonstrate this behavior in an experimental system, which also showed new features. It’s also great fun to have our report appear simultaneously with the report from my friend and colleague Raj Roy.”

Showalter and his WVU research collaborators, research assistant professor Mark Tinsley, Ph.D., and Simbarashe “Simba” Nkomo, a doctoral student, have published their findings in the prestigious journal Nature Physics. The three researchers designed the experiment together, Tinsley lead the computer simulations and Nkomo carried out the experiments.

A chimera state is a balanced system made up of synchronous and asynchronous oscillators. Oscillators are anything that exhibits cyclical behavior—AC circuits, neurons, cells, even clocks. When two or more oscillators interact, they can synchronize. For example, pendulum clocks placed on the same wall tend to keep time at the exact same pace. Cardiac pacemaker cells in the human heart fire at the same rate, resulting in spontaneous synchronization and a regular heartbeat. This type of synchronization arises from processes called global or local coupling, where all oscillators completely synchronize and act in concert.

In a chimera state, a different and unusual theoretical process called non-local coupling takes place. In non-local coupling, each element, for example a neuron, reacts more strongly to the signals of its closest neighbors and less strongly to distant neighbors. The idea of a dual synchronous and asynchronous system was puzzling to scientists who until a decade ago were focused primarily on the study of local and global coupling.

Showalter’s team used an oscillating chemical reaction in which the chemical particles periodically turn orange and green. The photosensitive reaction allowed each cycle’s phase to be manipulated—and the particles coupled—by controlling their exposure to light. In the experiment, one group of particles always synchronized, but depending on the strength of the particles’ coupling with its nearby neighbors, the second group either synchronized with the group, split into two different synchronized groups, formed a new type of behavior called a semi-synchronous state, or failed to synchronize at all, the chimera state. These states coexist even though every oscillator in the population is coupled to every other oscillator in the same manner. The Maryland researchers relied on an optical-feedback system, using light in a feedback loop to create an array of pixels in the chimera state.

Showalter speculates that there will be additional discoveries in other types of systems beyond the chemical and optical-feedback experiments.

“Many people are working in this area and I expect that we will see successful experiments reproducing chimera states in other systems soon, including mechanical systems and living systems like neural networks,” he said.

In the long run the reproduction and examination of the chimera state could lead researchers to a better understanding of neural networks and how the brain works. This could have implications for neuroscience and medicine.

“The exciting thing about this study is the possibilities that might open up in other research,” Showalter said. “You never know how prevalent or important a new class of dynamical behavior will be in the future.”

Showalter’s research was funded, in part, by a grant from the National Science Foundation.

For more information, please contact Kenneth Showalter at 304-293-0124 or via e-mail at kenneth.showalter@mail.wvu.edu.

-WVU-

rh/9/28/12

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