Introduction to Chaotic Intermittency

Replication of period-doubling route to chaos in impulsive systems

“…In study [22], intermittency was classified as type I, type II, and type III in accordance with the Floquet multipliers. Types I, II, and III respectively correpond to the formation of cyclic-fold bifurcation, sub-critical Hopf bifurcation or Neimark-Sacker bifurcation, and sub-critical perioddoubling bifurcation [23]. Some other kinds of intermittency are type X, type V, on-off, eyelet, crisisinduced, and ring [23]- [29].…”

“…Types I, II, and III respectively correpond to the formation of cyclic-fold bifurcation, sub-critical Hopf bifurcation or Neimark-Sacker bifurcation, and sub-critical perioddoubling bifurcation [23]. Some other kinds of intermittency are type X, type V, on-off, eyelet, crisisinduced, and ring [23]- [29]. The reader is referred to the studies [30]- [33] for some models possessing chaos through the intermittency route.…”

Characteristics of in-out intermittency in delay-coupled FitzHugh–Nagumo oscillators

“…Intermittency is a well-known phenomenon characterized by an alternation of time periods of regular or laminar dynamics, and irregular or turbulent bursts. The latter are seemingly randomly interspersed in the laminar phase and become more frequent with increasing distance from the transition to intermittency [1]. Starting from early studies involving fluctuating velocities in turbulent flows [2], the importance of intermittency has been well-recognized in several physical phenomena including forced nonlinear oscillators [3], plasma physics [4,5], Rayleigh-Bérnard convection [6,7], electronic circuits [8] and nonlinear Schrödinger equations [9].…”