Networks and Dynamical Processes

    Networks composed of vertices (or nodes) and edges (or links) provide a general framework for the representation of many different systems. First, any system with a discrete state space can be viewed as a network, in which the vertices represent the different states of the system and the edges correspond to possible transitions between these states. One example is provided by network representations of molecular motors. [1] [2] Second, composite systems that consist of many different but similiar components can also be viewed as networks, in which the vertices represent the different components and the edges correspond to "interactions" between these components. In general, the different components of the system can attain several internal states that evolve with time. The simplest case is provided by binary variables that can be active or inactive. [3] [4] At any given time, the state of the composite system is then characterized by an activity pattern of the network, and the system's dynamics is described by the time evolution of this pattern. Depending on the inital pattern, the system will reach one of the dynamical attractors that govern the system's long-time behavior.

  • J. Menche, A. Valleriani, and R. Lipowsky
    Sequences of phase transitions in Ising models on correlated networks.
    Phys. Rev. E 83, 061129 (2011). PDF (475 KB)

  • V. Bierbaum and R. Lipowsky
    Chemomechanical coupling and motor cycles of myosin V.
    Biophys. J. 100, 1747-1755 (2011). PDF (1 MB)

  • J. Menche, A. Valleriani, and R. Lipowsky
    Asymptotic properties of degree-correlated scale-free networks.
    Phys. Rev. E 81, 046103 (2010). PDF (885 KB)

  • S. Liepelt and R. Lipowsky
    Impact of slip cycles on the operation modes and efficiency of molecular motors.
    J. Stat. Phys. 141, 1-16 (2010). PDF (561 KB)

  • J. Menche, A. Valleriani, and R. Lipowsky
    Dynamical processes on dissortative scale-free networks.
    EPL 89, 18002 (2010). PDF (496 KB)

  • R. Lipowsky, S. Liepelt, and A. Valleriani
    Energy conversion by molecular motors coupled to nucleotide hydrolysis.
    J. Stat. Phys. 135, 951-975 (2009). PDF (752 KB)

  • S. Liepelt and R. Lipowsky
    Kinesin's network of chemomechanical motor cycles.
    Phys. Rev. Lett. 98, 258102 (2007). PDF (376 KB)
    Appendices: PDF (220 KB)

  • S. Liepelt and R. Lipowsky
    Steady-state balance conditions for molecular motor cycles and stochastic nonequilibrium processes.
    EPL 77, 50002 (2007). PDF (256 KB)

  • H. Zhou and R. Lipowsky
    Activity patterns on random scale-free networks: global dynamics arising from local majority rules.
    J. Stat. Mech. - Theo. & Exp. P01009 (2007). PDF (1.1 MB)

  • H. Zhou and R. Lipowsky
    Dynamic pattern evolution on scale-free networks.
    PNAS 102, 10052 - 10057 (2005). PDF (252 KB)
    Supporting Information: PDF (476 KB)

  • H. Zhou and R. Lipowsky
    Network Brownian Motion: A New Method to Measure Vertex-Vertex Proximity and to Identify Communities and Subcommunities.
    Lecture Notes Comp. Science 3038, 1062-1069 (2004). PDF (200 KB)

  • R. Lipowsky and S. Klumpp
    'Life is Motion': Multiscale motility of molecular motors.
    Physica A 352, 53-112, (2005). PDF (868 KB)

  • R. Lipowsky.
    Universal aspects of the chemo-mechanical coupling for molecular motors.
    Phys. Rev. Lett. 85 , 4401-4404 (2000). PDF (92 KB)