Discrete breathers in integrate-and-fire oscillator networks

A number of novel dynamical patterns are found in an integrate-and-fire network, including periodic breathers with single, double, and triple wavefronts, and chaotic breathers. It is found that the periodic breathers always propagate whereas the chaotic ones always remain stationary. A novel route to chaotic breathers through intermittency is identified, as opposed to the paths through quasi-periodicity and period-doubling mostly discussed in dissipative lattice systems. The system is found to display prominent bistability, resulting in "hysteresis" loops in single-oscillator inter-spike intervals as the parameter varies.