1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Disorder-induced dynamics in a pair of coupled heterogeneous phase oscillator networks
Rent:
Rent this article for
USD
10.1063/1.4758814
/content/aip/journal/chaos/22/4/10.1063/1.4758814
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/4/10.1063/1.4758814
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Bifurcation set of Eqs. (7)–(9) for small heterogeneity. Curves of the three local bifurcations are labelled in the figure. Squares: homoclinic bifurcation of and , destroying and . Circles: symmetric homoclinic connection to S, gluing and together to form . Stars: symmetric heteroclinic bifurcation of and , destroying .

Image of FIG. 2.
FIG. 2.

Typical examples of the periodic orbits (top, when A = 0.35) and (bottom, when A = 0.5). The left column shows time series of (solid) and (dashed) and the right panels show orbits in the plane. Other parameters: D = 0.0005.

Image of FIG. 3.
FIG. 3.

Circles joined by lines: the gluing bifurcation shown in Fig. 1. Solid lines are contours of equal values of the saddle index for S, , where the eigenvalues of the Jacobian at S are . Note that the zero contour corresponds to the pitchfork bifurcation curve shown in Fig. 1.

Image of FIG. 4.
FIG. 4.

Dynamics of the phase oscillator network (1) and (2) for N = 300 at (top to bottom) A = 0.05, 0.15, 0.35, 0.45, when D = 0.0007. Left panelsshow , colour-coded; right panels show and , where and . Parameters: .

Image of FIG. 5.
FIG. 5.

Bifurcation set of Eqs. (7)–(9) for . Curves of the three local bifurcations are labelled in the figure. Circles: symmetric homoclinic connection to S, gluing and together. Crosses: saddle-node bifurcation of the periodic orbit (and of .) The thin line labelled “1” is the curve on which the saddle index changes from less than 1 (below the curve) to greater than 1 (above the curve).

Image of FIG. 6.
FIG. 6.

Parameter sweeps of Eqs. (7)–(9) for A decreasing (panels a and b) and increasing (c and d), when . Panels a and c show the value of when increases through 0.5 during a long simulation and after transients have died out. Panels b and d show the most positive Lyapunov exponent of the solution.

Image of FIG. 7.
FIG. 7.

Largest Lyapunov exponent for Eqs. (7)–(9) as a function of D and A. Other curves are: dashed: gluing bifurcation; solid: ; dash-dotted: Hopf; crosses joined by lines: saddle-node bifurcation of periodic orbits. Compare with Fig. 5.

Image of FIG. 8.
FIG. 8.

The largest Lyapunov exponent for the network (1) and (2) with N = 100 and D = 0.004.

Image of FIG. 9.
FIG. 9.

(a): Behaviour of the network (1) and (2) at A = 0.15 ( is shown colour-coded). (b): (solid blue) and (dashed green) as functions of time for the state in the top panel, where and . (c) and (d): Lyapunov spectrum, i.e., all 2N Lyapunov exponents, for the state shown here. [(d) is an enlargement of the rightmost part of (c).] Parameters: N = 100 and D = 0.004.

Image of FIG. 10.
FIG. 10.

(a): Behaviour of the network (1) and (2) at A = 0.4 ( is shown colour-coded). (b): (solid blue) and (dashed green) as functions of time for the state in the top panel, where and . (c) and (d): Lyapunov spectrum, i.e., all 2N Lyapunov exponents, for the state shown here. [(d) is an enlargement of the rightmost part of (c).] Parameters: N = 100 and D = 0.004.

Image of FIG. 11.
FIG. 11.

Left column: (solid) and (dashed) from numerically solving Eqs. (20) and (21) for (top), (middle), and (bottom). Right column: (solid) and (dashed), where and , for the same noise intensities as in the left column. Parameters: .

Loading

Article metrics loading...

/content/aip/journal/chaos/22/4/10.1063/1.4758814
2012-10-17
2014-04-23
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Disorder-induced dynamics in a pair of coupled heterogeneous phase oscillator networks
http://aip.metastore.ingenta.com/content/aip/journal/chaos/22/4/10.1063/1.4758814
10.1063/1.4758814
SEARCH_EXPAND_ITEM