CHAOS IN THE MODEL OF REPETITIVE PHASE-TRANSITIONS WITH HYSTERESIS - APPLICATION TO THE SELF-SUSTAINED POTENTIAL OSCILLATIONS OF LIPID-BILAYER MEMBRANES INDUCED BY GEL LIQUID-CRYSTAL PHASE-TRANSITIONS
K. Yagisawa et al., CHAOS IN THE MODEL OF REPETITIVE PHASE-TRANSITIONS WITH HYSTERESIS - APPLICATION TO THE SELF-SUSTAINED POTENTIAL OSCILLATIONS OF LIPID-BILAYER MEMBRANES INDUCED BY GEL LIQUID-CRYSTAL PHASE-TRANSITIONS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(2), 1994, pp. 1320-1335
To clarify the mechanism of chaos generation and the routes to chaos i
n the self-sustained oscillation of the electric potential difference
between two solutions divided by a lipid-bilayer membrane, a simple mo
del of the system, the model of repetitive phase transitions with hyst
eresis, is presented in which oscillation is driven by repetitive gel-
liquid-crystal phase transitions with hysteresis occurring in the lipi
d membrane and at the same time by a periodic external current. The dy
namical property of the system is completely described by the nature o
f the function mapping the times at which the phase transition occurs
successively. There exist various kinds of routes to chaos in the mode
l of repetitive phase transitions with hysteresis (RPTH model) such as
the period-doubling cascades, the intermittency, the quasiperiodic-ch
aotic transition, and the transition to chaos from complete phase lock
ing. When the values of the system parameters satisfy certain conditio
ns, the RPTH model becomes equivalent to the integrate-and-fire model
and similar to the driven-relaxation-oscillator model. The model also
generates structurally stable chaotic attractors which are never destr
oyed by a slight change in the values of system parameters. The attrac
tors appear only for the regions of parameter values where the mapping
function has at least one discontinuous point. This model contains th
e essential features of evolution behavior in various kinds of systems
which generate iterative phase transitions with hysteresis.