TY  - JOUR
A1  - Abel, M. W.
A1  - Shepelyansky, Dima L.
T1  - Google matrix of business process management
JF  - The European physical journal : B, Condensed matter and complex systems
N2  - Development of efficient business process models and determination of their characteristic properties are subject of intense interdisciplinary research. Here, we consider a business process model as a directed graph. Its nodes correspond to the units identified by the modeler and the link direction indicates the causal dependencies between units. It is of primary interest to obtain the stationary flow on such a directed graph, which corresponds to the steady-state of a firm during the business process. Following the ideas developed recently for the World Wide Web, we construct the Google matrix for our business process model and analyze its spectral properties. The importance of nodes is characterized by PageRank and recently proposed CheiRank and 2DRank, respectively. The results show that this two-dimensional ranking gives a significant information about the influence and communication properties of business model units. We argue that the Google matrix method, described here, provides a new efficient tool helping companies to make their decisions on how to evolve in the exceedingly dynamic global market.
Y1  - 2011
U6  - https://doi.org/10.1140/epjb/e2010-10710-y
SN  - 1434-6028
VL  - 84
IS  - 4
SP  - 493
EP  - 500
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Mulansky, Mario
A1  - Ahnert, Karsten
A1  - Pikovskij, Arkadij
A1  - Shepelyansky, Dima L.
T1  - Strong and weak chaos in weakly nonintegrable many-body hamiltonian systems
JF  - Journal of statistical physics
N2  - We study properties of chaos in generic one-dimensional nonlinear Hamiltonian lattices comprised of weakly coupled nonlinear oscillators by numerical simulations of continuous-time systems and symplectic maps. For small coupling, the measure of chaos is found to be proportional to the coupling strength and lattice length, with the typical maximal Lyapunov exponent being proportional to the square root of coupling. This strong chaos appears as a result of triplet resonances between nearby modes. In addition to strong chaos we observe a weakly chaotic component having much smaller Lyapunov exponent, the measure of which drops approximately as a square of the coupling strength down to smallest couplings we were able to reach. We argue that this weak chaos is linked to the regime of fast Arnold diffusion discussed by Chirikov and Vecheslavov. In disordered lattices of large size we find a subdiffusive spreading of initially localized wave packets over larger and larger number of modes. The relations between the exponent of this spreading and the exponent in the dependence of the fast Arnold diffusion on coupling strength are analyzed. We also trace parallels between the slow spreading of chaos and deterministic rheology.
KW  - Lyapunov exponent
KW  - Arnold diffusion
KW  - Chaos spreading
Y1  - 2011
U6  - https://doi.org/10.1007/s10955-011-0335-3
SN  - 0022-4715
VL  - 145
IS  - 5
SP  - 1256
EP  - 1274
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Zhirov, O. V.
A1  - Pikovskij, Arkadij
A1  - Shepelyansky, Dima L.
T1  - Quantum vacuum of strongly nonlinear lattices
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We study the properties of classical and quantum strongly nonlinear chains by means of extensive numerical simulations. Due to strong nonlinearity, the classical dynamics of such chains remains chaotic at arbitrarily low energies. We show that the collective excitations of classical chains are described by sound waves whose decay rate scales algebraically with the wave number with a generic exponent value. The properties of the quantum chains are studied by the quantum Monte Carlo method and it is found that the low-energy excitations are well described by effective phonon modes with the sound velocity dependent on an effective Planck constant. Our results show that at low energies the quantum effects lead to a suppression of chaos and drive the system to a quasi-integrable regime of effective phonon modes.
Y1  - 2011
U6  - https://doi.org/10.1103/PhysRevE.83.016202
SN  - 1539-3755
VL  - 83
IS  - 1
PB  - American Physical Society
CY  - College Park
ER  -