TY  - JOUR
A1  - Krämer, Kai Hauke
A1  - Hellmann, Frank
A1  - Anvari, Mehrnaz
A1  - Kurths, Jürgen
A1  - Marwan, Norbert
T1  - Spike spectra for recurrences
JF  - Entropy : an international and interdisciplinary journal of entropy and information studies
N2  - In recurrence analysis, the tau-recurrence rate encodes the periods of the cycles of the underlying high-dimensional time series. It, thus, plays a similar role to the autocorrelation for scalar time-series in encoding temporal correlations. 
However, its Fourier decomposition does not have a clean interpretation. Thus, there is no satisfactory analogue to the power spectrum in recurrence analysis. 
We introduce a novel method to decompose the tau-recurrence rate using an over-complete basis of Dirac combs together with sparsity regularization. 
We show that this decomposition, the inter-spike spectrum, naturally provides an analogue to the power spectrum for recurrence analysis in the sense that it reveals the dominant periodicities of the underlying time series. 
We show that the inter-spike spectrum correctly identifies patterns and transitions in the underlying system in a wide variety of examples and is robust to measurement noise.
KW  - decomposition
KW  - frequency analysis
KW  - recurrence analysis
KW  - bifurcations
Y1  - 2022
U6  - https://doi.org/10.3390/e24111689
SN  - 1099-4300
VL  - 24
IS  - 11
PB  - MDPI
CY  - Basel
ER  - 
TY  - JOUR
A1  - Frasca, Mattia
A1  - Bergner, Andre
A1  - Kurths, Jürgen
A1  - Fortuna, Luigi
T1  - Bifurcations in a star-like network of Stuart-Landau oscillators
JF  - International journal of bifurcation and chaos : in applied sciences and engineering
N2  - In this paper, we analytically study a star motif of Stuart-Landau oscillators, derive the bifurcation diagram and discuss the different forms of synchronization arising in such a system. Despite the parameter mismatch between the central node and the peripheral ones, an analytical approach independent of the number of units in the system has been proposed. The approach allows to calculate the separatrices between the regions with distinct dynamical behavior and to determine the nature of the different transitions to synchronization appearing in the system. The theoretical analysis is supported by numerical results.
KW  - Complex networks
KW  - synchronization
KW  - bifurcations
Y1  - 2012
U6  - https://doi.org/10.1142/S0218127412501738
SN  - 0218-1274
VL  - 22
IS  - 7
PB  - World Scientific
CY  - Singapore
ER  -