# On the origin of self-oscillations in large systems

@article{Martino2018OnTO, title={On the origin of self-oscillations in large systems}, author={Daniele De Martino}, journal={arXiv: Statistical Mechanics}, year={2018} }

In this article is shown that large systems endowing phase coexistence display self-oscillations in presence of linear feedback between the control and order parameters, where an Andronov-Hopf bifurcation takes over the phase transition. This is simply illustrated through the mean field Landau theory whose feedback dynamics turns out to be described by the Van der Pol equation and it is then validated for the fully connected Ising model following heat bath dynamics. Despite its simplicity, thisβ¦Β

## References

SHOWING 1-10 OF 53 REFERENCES

### Ginzburg-Landau approximation for self-sustained oscillators weakly coupled on complex directed graphs

- MathematicsCommun. Nonlinear Sci. Numer. Simul.
- 2018

### A minimal model for congestion phenomena on complex networks

- Computer Science
- 2009

The model reproduces the crossover in the scaling of traffic fluctuations empirically observed in the Internet, and moreover, a conserved version can reproduce qualitatively some stylized facts of traffic in transportation networks.

### COUPLED SELF-OSCILLATING SYSTEMS: THEORY AND APPLICATIONS

- Physics
- 2009

The structure of self-oscillating dynamical systems is reviewed, and some basic applications to speech generation, hydrodynamic instabilities, volcanic tremor are discussed.

### Controllability of complex networks

- Computer ScienceNature
- 2011

Analytical tools are developed to study the controllability of an arbitrary complex directed network, identifying the set of driver nodes with time-dependent control that can guide the systemβs entire dynamics.

### Sustained oscillations in living cells

- BiologyNature
- 1999

It is shown, using a suspension of yeast cells, that living cells can be kept in a well defined oscillating state indefinitely when starved cells, glucose and cyanide are pumped into a cuvette with outflow of surplus liquid.

### Congestion phenomena on complex networks

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

It is found that traffic control improves global performance, enlarging the free-flow region in parameter space only in heterogeneous networks.

### Nonequilibrium statistical mechanics of the zero-range process and related models

- Mathematics
- 2005

We review recent progress on the zero-range process, a model of interacting particles which hop between the sites of a lattice with rates that depend on the occupancy of the departure site. Weβ¦

### The effect of network structure on phase transitions in queuing networks

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

The aim is to establish a direct connection between the structure of an uncorrelated random graph with quenched disorder and the value of the critical traffic load and it is shown that if the network is dense, the quenches and annealed formulas for the critical loading probability coincide.

### Critical behavior of entropy production and learning rate: Ising model with an oscillating field

- Physics
- 2016

We study the critical behavior of the entropy production of the Ising model subject to a magnetic field that oscillates in time. The mean-field model displays a phase transition that can be eitherβ¦

### Biological rhythms and the behavior of populations of coupled oscillators.

- BiologyJournal of theoretical biology
- 1967