310 research outputs found
Oscillation death in coupled counter-rotating identical nonlinear oscillators
We study oscillatory and oscillation suppressed phases in coupled
counter-rotating nonlinear oscillators. We demonstrate the existence of limit
cycle, amplitude death, and oscillation death, and also clarify the Hopf,
pitchfork, and infinite period bifurcations between them. Especially, the
oscillation death is a new type of oscillation suppressions of which the
inhomogeneous steady states are neutrally stable. We discuss the robust neutral
stability of the oscillation death in non-conservative systems via the
anti-PT-symmetric phase transitions at exceptional points in terms of
non-Hermitian systems.Comment: 7 pages, 4 figure
Conjugate coupling induced symmetry breaking and quenched oscillations
Spontaneous symmetry breaking (SSB) is essential and plays a vital role many
natural phenomena, including the formation of Turing pattern in organisms and
complex patterns in brain dynamics. In this work, we investigate whether a set
of coupled Stuart-Landau oscillators can exhibit spontaneous symmetry breaking
when the oscillators are interacting through dissimilar variables or conjugate
coupling. We find the emergence of SSB state with coexisting distinct dynamical
states in the parametric space and show how the system transits from symmetry
breaking state to out-of-phase synchronized (OPS) state while admitting
multistabilities among the dynamical states. Further, we also investigate the
effect of feedback factor on SSB as well as oscillation quenching states and we
point out that the decreasing feedback factor completely suppresses SSB and
oscillation death states. Interestingly, we also find the feedback factor
completely diminishes only symmetry breaking oscillation and oscillation death
(OD) states but it does not affect the nontrivial amplitude death (NAD) state.
Finally, we have deduced the analytical stability conditions for in-phase and
out-of-phase oscillations, as well as amplitude and oscillation death states.Comment: Accepted for publication in Europhysics Letter
Bifurcation in cell cycle dynamics regulated by p53
We study the regulating mechanism of p53 on the properties of cell cycle
dynamics in the light of the proposed model of interacting p53 and cell cycle
networks via p53. Irradiation (IR) introduce to p53 compel p53 dynamics to
suffer different phases, namely oscillating and oscillation death (stabilized)
phases. The IR induced p53 dynamics undergo collapse of oscillation with
collapse time \Delta t which depends on IR strength. The stress p53 via IR
drive cell cycle molecular species MPF and cyclin dynamics to different states,
namely, oscillation death, oscillations of periods, chaotic and sustain
oscillation in their bifurcation diagram. We predict that there could be a
critical \Delta t_c induced by p53 via IR_c, where, if \Delta t < \Delta t_c
the cell cycle may come back to normal state, otherwise it will go to cell
cycle arrest (apoptosis)
Diverse routes to oscillation death in a coupled-oscillator system.
We study oscillation death (OD) in a well-known coupled-oscillator system that has been used to model cardiovascular phenomena. We derive exact analytic conditions that allow the prediction of OD through the two known bifurcation routes, in the same model, and for different numbers of coupled oscillators. Our exact analytic results enable us to generalize OD as a multiparameter-sensitive phenomenon. It can be induced, not only by changes in couplings, but also by changes in the oscillator frequencies or amplitudes. We observe synchronization transitions as a function of coupling and confirm the robustness of the phenomena in the presence of noise. Numerical and analogue simulations are in good agreement with the theory
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