# Dynamic states of a unidirectional ring of chen oscillators

## Abstract

We study curious dynamical patterns appearing in a network of a unidirectional ring of Chen oscillators coupled to a ‘buffer’ cell. The network has Z{sub 3} exact symmetry group. We simulate the coupled cell systems associated to the two networks and obtain steady-states, rotating waves, quasiperiodic behavior, and chaos. The different patterns appear to arise through a sequence of Hopf, period-doubling and period-halving bifurcations. The network architecture appears to explain some patterns, whereas the properties of the chaotic oscillator may explain others. We use XPPAUT and MATLAB to compute numerically the relevant states.

- Authors:

- Faculty of Sciences, University of Porto, Rua do Campo Alegre s/n, 4440-452 Porto, Portugal up200802541@fc.up.pt (Portugal)
- School of Engineering, Polytechnic of Porto, Rua Dr António Bernardino de Almeida, 431, 4200-072 Porto, Portugal cap@isep.ipp.pt (Portugal)

- Publication Date:

- OSTI Identifier:
- 22391079

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1648; Journal Issue: 1; Conference: ICNAAM-2014: International Conference on Numerical Analysis and Applied Mathematics 2014, Rhodes (Greece), 22-28 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; CHAOS THEORY; COMPUTERIZED SIMULATION; M CODES; OSCILLATORS; STEADY-STATE CONDITIONS; SYMMETRY GROUPS; X CODES

### Citation Formats

```
Carvalho, Ana, and Pinto, Carla M.A.
```*Dynamic states of a unidirectional ring of chen oscillators*. United States: N. p., 2015.
Web. doi:10.1063/1.4912580.

```
Carvalho, Ana, & Pinto, Carla M.A.
```*Dynamic states of a unidirectional ring of chen oscillators*. United States. doi:10.1063/1.4912580.

```
Carvalho, Ana, and Pinto, Carla M.A. Tue .
"Dynamic states of a unidirectional ring of chen oscillators". United States.
doi:10.1063/1.4912580.
```

```
@article{osti_22391079,
```

title = {Dynamic states of a unidirectional ring of chen oscillators},

author = {Carvalho, Ana and Pinto, Carla M.A.},

abstractNote = {We study curious dynamical patterns appearing in a network of a unidirectional ring of Chen oscillators coupled to a ‘buffer’ cell. The network has Z{sub 3} exact symmetry group. We simulate the coupled cell systems associated to the two networks and obtain steady-states, rotating waves, quasiperiodic behavior, and chaos. The different patterns appear to arise through a sequence of Hopf, period-doubling and period-halving bifurcations. The network architecture appears to explain some patterns, whereas the properties of the chaotic oscillator may explain others. We use XPPAUT and MATLAB to compute numerically the relevant states.},

doi = {10.1063/1.4912580},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1648,

place = {United States},

year = {Tue Mar 10 00:00:00 EDT 2015},

month = {Tue Mar 10 00:00:00 EDT 2015}

}

DOI: 10.1063/1.4912580

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