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Sophisticated methods for analysing complex networks promise to be of great benefit to almost all scientific disciplines, yet they elude us. In this work, we make fundamental methodological advances to rectify this. We discover that the interaction between a small number of roles, played by nodes in a network, can characterize a network's structure and also… (More)

- Zoran Levnajić, Igor Mezić
- 2006

———————————————————————————————————————-We present a computational study of the invariant sets visualization method based on ergodic partition theory, firstly proposed in [1]. The algorithms for computation of the time averages of many L 1 functions are developed and employed producing the approximation of the phase space ergodic partitioning. The method is… (More)

- Zoran Levnajić, Igor Mezić
- 2008

—————————————————————————————————————————-We extend the computational visualization method proposed in [1, 2] using the concept of the harmonic time averages presented in [3]. Algorithms for frequency analysis of the phase space are constructed and implemented numerically, producing a graphical visualization of the periodic sets for a given periodicity. The… (More)

- Zoran Levnajić
- 2013

We propose a conceptually novel method of reconstructing the topology of dynamical networks. By examining the correlation between the variable of one node and the derivative of another node's variable, we derive a simple matrix equation yielding the network adjacency matrix. Our assumptions are the possession of time series describing the network dynamics,… (More)

Evolutionary optimisation algorithm is employed to design networks of phase-repulsive oscillators that achieve an anti-phase synchronised state. By introducing the link frustration, the evolutionary process is implemented by rewiring the links with probability proportional to their frustration, until the final network displaying a unique non-frustrated… (More)

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