Design of external forces for eliminating traveling wave in a piecewise linear FitzHugh–Nagumo model

Abstract

Elimination and control of nonlinear phenomena in excitable media are important for academic interests and practical applications. This paper provides a systematic procedure to design external forces for eliminating a traveling wave in a one-dimensional piecewise linear FitzHugh-Nagumo model. This procedure allows us to design nonfeedback and feedback control systems. The feedback control systems are designed using classical control theory. Furthermore, this procedure is extended to a two-dimensional model and verified using numerical simulation.

System identification of propagating wave segments in excitable media and its application to advanced control

“…The elimination and control of turbulence, spirals, and propagating waves in excitable media have been widely studied. Recent studies have shown that these phenomena can be eliminated by external forces without feedback [7][8][9][10][11] or with feedback [12][13][14]. In addition to elimination, the control of waves and patterns in excitable media has also been actively investigated [15,16].…”

Proportional-integral control of propagating wave segments in excitable media

“…Several methods have been proposed for eliminating nonlinear phenomena, including global nonfeedback control [14][15][16][17][18], local nonfeedback control [19][20][21][22][23][24][25][26][27][28][29][30][31][32], global feedback control [33][34][35], and local feedback control [36]. Moreover, numerous studies have shown theoretically and experimentally that waves and patterns can be controlled [37,38].…”