Collective Dynamical Behaviors of Nonlocally Coupled Brockett Oscillators

Figure 2

Space-time diagram and snapshot of nonlocally coupled Brockett oscillators with attractive and repulsive couplings for (a) transient desynchronized state , (b) transient chimera , (c) transient traveling wave , (d) traveling wave , (i) synchronized state , (j) cluster oscillatory state , (k) cluster oscillation death , and (l) chimera death . In the space-time diagram, the lower portion is obtained after transient time units, and the upper portion is observed after transient time units. The second panel (e–h) and fourth panel (m–p) are the corresponding snapshots of first panel (a–d) and third panel (i–l), respectively. Lower transients display the dynamical transition from desynchronized state to chimera death through transient chimera, transient traveling waves, synchronization, cluster oscillatory states, and cluster oscillation death states for the given coupling strength, whereas larger transients exhibit the transition from synchronized state to chimera death through the traveling wave state and cluster oscillation death states. Other parameters are fixed as , , , and .

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)