Cardiac alternans is a marker of sudden cardiac arrest, the leading cause of death in the United States that kills hundreds of thousands of Americans each year. In the language of nonlinear dynamics, the onset of cardiac alternans is induced by a period-doubling bifurcation. In this work, we explore the bifurcation and control of cardiac alternans in a fiber based on numerical analyses of the seminal amplitude equation derived by Echebarria and Karma. First, we seek the solution of the amplitude equation using a series expansion. Then, detailed numerical bifurcation analyses are carried out to illustrate the spatiotemporal patterns of cardiac alternans. We demonstrate that secondary bifurcations lead to multiple unstable patterns, which impose difficulties in feedback control of alternans. Effects and limitations of feedback control algorithms are explored. The theoretical analyses here help to improve the understanding of the mechanisms of alternans in cardiac tissue.

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