Ageing in mixed populations of Stuart–Landau oscillators: the role of diversity

Abstract

The phenomenon of ageing in a population of autonomous oscillators, namely the increase in the number of inactive (or non-oscillatory) units due to coupling interactions is studied in a population of globally coupled Stuart–Landau oscillators. The initial populations are prepared either as a mixture of active and inactive oscillators or as an ensemble of active oscillators with a mixture of distinct frequencies. The ageing transition does not depend on whether the coupling breaks gauge symmetry or not, but is affected by the degree of diversity in the ensemble, namely the existence of different types of subsystems that can cause oscillation quenching when coupled. The scaling exponents depend on the nature of the coupling interaction.

Stasis in heterogeneous networks of coupled oscillators: discontinuous transition with hysteresis

“…Along C, the abrupt jump to stasis occur at pc 1 ≈ 0.7 and is always initial condition dependent, whereas in backward sweep an abrupt transition from stasis to active occurs at pc 2 ≈ 0.48 which remains constant regardless of initial conditions. continuous along the lines A and B in figure 2(a), and as can be seen in figure 4(a), the order parameter obeys a power law scaling [1,11]…”

“…The increase in the dimensionality of the constituent units does not, in the present instance, bring new dynamical features into play, but it offers the possibility of new bifurcations, and new active dynamical states-such as chaotic attractors-that could potentially exhibit new collective behaviour. This is currently under investigation [31]. 10) and ( 11) using the mean field analysis, namely Kc ≈ 2.8 for α = 1 figure 5(g).…”

“…Studies of the dynamics of heterogeneous ensembles of dynamical systems have practical relevance to a variety of problems in the physical and biological sciences. The models that have been studied so far in this context [1,11,13,20,26] have typically used a model oscillator with a single parameter controlling the dynamics: by varying the parameter one has either active (oscillatory) or inactive (fixed point) dynamics. When coupled, there are either global oscillations or global oscillation death and the transition to this latter state has been described as an ageing process which is also termed a transition to stasis [11].…”

“…In an effort to understand the origin of this transition-which does not appear to be the consequence of a simple majority rule-a number of variations of the initial model [1] have been studied, by incorporating distributed time delays [4,5], by varying the network topology [6,7], or by introducing heterogeneity in the parameters [8,9] as well as by including noise [10]. The nature of the coupling between the oscillators-whether through similar or dissimilar variables [11,12]-has also been explored in some detail over the past few years. One conclusion that can be drawn from this large variety of studies is that the essential feature that is required in an ensemble that exhibits the transition to stasis or ageing is heterogeneity or diversity in the components or in the interactions: some form of dynamical frustration seems necessary.…”

Preface: Long-range interactions and synchronization

“…• The paper [8] 'ageing in mixed populations of Stuart-Landau oscillators: the role of diversity' by Sahoo et al studies the question of ageing transition in a population of globally coupled Stuart-Landau oscillators, namely, the increase in time of the number of inactive (or non-oscillatory) units. The system has an initial population that is either a mixture of active and inactive oscillators or an ensemble of active oscillators with a mixture of distinct frequencies.…”