# Two scenarios for the onset and suppression of collective oscillations in heterogeneous populations of active rotators.

@article{Klinshov2019TwoSF, title={Two scenarios for the onset and suppression of collective oscillations in heterogeneous populations of active rotators.}, author={Vladimir V. Klinshov and Igor Franovi'c}, journal={Physical review. E}, year={2019}, volume={100 6-1}, pages={ 062211 } }

We consider the macroscopic regimes and the scenarios for the onset and the suppression of collective oscillations in a heterogeneous population of active rotators composed of excitable or oscillatory elements. We analyze the system in the continuum limit within the framework of Ott-Antonsen reduction method, determining the states with a constant mean field and their stability boundaries in terms of the characteristics of the rotators' frequency distribution. The system is established to…

## 9 Citations

### Collective Activity Bursting in a Population of Excitable Units Adaptively Coupled to a Pool of Resources

- BiologyFrontiers in Network Physiology
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This work combines the Ott-Antonsen reduction for the collective dynamics of the population and singular perturbation theory to obtain a reduced system describing the interaction between the population mean field and the resources.

### D ec 2 01 9 Ott-Antonsen ansatz is the only admissible truncation of a circular cumulant series

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The cumulant representation is common in classical statistical physics for variables on the real line and the issue of closures of cumulant expansions is well elaborated. The case of phase variables…

### A global bifurcation organizing rhythmic activity in a coupled network.

- MathematicsChaos
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We study a system of coupled phase oscillators near a saddle-node on invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system…

### Collective activity bursting in networks of excitable systems adaptively coupled to a pool of resources

- Computer Science
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This work combines the Ott-Antonsen reduction for the collective dynamics of the network and singular perturbation theory to obtain a reduced system describing the interaction between the network mean field and the resources.

### Noise-induced dynamical regimes in a system of globally coupled excitable units.

- PhysicsChaos
- 2021

It is shown how characteristic quantities such as macroscopic and microscopic variability of interspike intervals can depend in a non-monotonous way on the noise level.

### Effect of noise on the collective dynamics of a heterogeneous population of active rotators.

- MathematicsChaos
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With numerical simulation, a decent accuracy is confirmed of the model reduction for a moderate noise strength; in particular, it correctly predicts the location of the bistability domains in the parameter space.

### Collective in-plane magnetization in a two-dimensional XY macrospin system within the framework of generalized Ott–Antonsen theory

- PhysicsPhilosophical Transactions of the Royal Society A
- 2020

It is shown that inside the temperature interval of existence of the AF phase, a static external field tilted to the plane of the array is able to induce first-order phase transitions from AF to ferromagnetic state; the phase diagrams displaying stable and metastable regions of the system are presented.

### Collective in-plane magnetization in a 2D XY macrospin system within the framework of generalized Ott-Antonsen theory

- Physics
- 2019

The problem of magnetic transitions between the low-temperature (macrospin ordered) phases in 2D XY arrays is addressed. The system is modeled as a plane structure of identical single-domain…

### Ott-Antonsen ansatz truncation of a circular cumulant series

- MathematicsPhysical Review Research
- 2019

The cumulant representation is common in classical statistical physics for variables on the real line and the issue of closures of cumulant expansions is well elaborated. The case of phase variables…

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