  We study collective helping behavior and bystander effects in a coevolving
helping network model. A node and a link of the network represents an agent who
renders or receives help and a friendly relation between agents, respectively.
A helping trial of an agent depends on relations with other involved agents and
its result (success or failure) updates the relation between the helper and the
recipient. We study the network link dynamics and its steady states
analytically and numerically. The full phase diagram is presented with various
kinds of active and inactive phases and the nature of phase transitions are
explored. We find various interesting bystander effects, consistent with the
field study results, of which the underlying mechanism is proposed.
