  We investigate macroscopic behavior of a dynamical network consisting of a
time-evolving wiring of interactions among a group of random walkers. We assume
that each walker (agent) has an oscillator and show that depending upon the
nature of interaction, synchronization arises where each of the individual
oscillators are allowed to move in such a random walk manner in a finite region
of three dimensional space. Here the vision range of each oscillator decides
the number of oscillators with which it interacts. The live interaction between
the oscillators is of intermediate type ( i.e., not local as well as not
global) and may or may not be bidirectional. We analytically derive density
dependent threshold of coupling strength for synchronization using linear
stability analysis and numerically verify the obtained analytical results.
Additionally, we explore the concept of basin stability, a nonlinear measure
based on volumes of basin of attractions, to investigate how stable the
synchronous state is under large perturbations. The synchronization phenomenon
is analyzed taking limit cycle and chaotic oscillators for wide ranges of
parameters like interaction strength k between the walkers, speed of movement v
and vision range r.
