6 research outputs found
Hierarchy and Polysynchrony in an adaptive network
We describe a simple adaptive network of coupled chaotic maps. The network
reaches a stationary state (frozen topology) for all values of the coupling
parameter, although the dynamics of the maps at the nodes of the network can be
non-trivial. The structure of the network shows interesting hierarchical
properties and in certain parameter regions the dynamics is polysynchronous:
nodes can be divided in differently synchronized classes but contrary to
cluster synchronization, nodes in the same class need not be connected to each
other. These complicated synchrony patterns have been conjectured to play roles
in systems biology and circuits. The adaptive system we study describes ways
whereby this behaviour can evolve from undifferentiated nodes.Comment: 13 pages, 17 figure
Families of piecewise linear maps with constant Lyapunov exponent
We consider families of piecewise linear maps in which the moduli of the two
slopes take different values. In some parameter regions, despite the variations
in the dynamics, the Lyapunov exponent and the topological entropy remain
constant. We provide numerical evidence of this fact and we prove it
analytically for some special cases. The mechanism is very different from that
of the logistic map and we conjecture that the Lyapunov plateaus reflect
arithmetic relations between the slopes.Comment: 26 pages, 13 figure
Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems
We describe the dynamics of a simple adaptive network. The network
architecture evolves to a number of disconnected components on which the
dynamics is characterized by the possibility of differently synchronized nodes
within the same network (polysynchronous states). These systems may have
implications for the evolutionary emergence of polysynchrony and hierarchical
networks in physical or biological systems modeled by adaptive networks.Comment: 4 pages, 4 figure