Math. Model. Nat. Phenom.
Volume 8, Number 6, 2013Ecology
|Page(s)||5 - 24|
|Published online||28 November 2013|
The Effect of Different Communication Mechanisms on the Movement and Structure of Self-Organised Aggregations
Department of Mathematics, University of
Corresponding author. E-mail: firstname.lastname@example.org
The formation, persistence and movement of self-organised biological aggregations are mediated by signals (e.g., visual, acoustic or chemical) that organisms use to communicate with each other. To investigate the effect that communication has on the movement of biological aggregations, we use a class of nonlocal hyperbolic models that incorporate social interactions and different communication mechanisms between group members. We approximate the maximum speed for left-moving and right-moving groups, and show numerically that the travelling pulses exhibited by the nonlocal hyperbolic models actually travel at this maximum speed. Next, we use the formula for the speed of a travelling pulse to calculate the reversal time for the zigzagging behaviour, and show that the communication mechanisms have an effect on these reversal times. Moreover, we show that how animals communicate with each other affects also the density structure of the zigzags. These findings offer a new perspective on the complexity of the biological factors behind the formation and movement of various aggregations.
Mathematics Subject Classification: 92D50 / 92-08 / 35Lxx
Key words: travelling pulses / zigzag pulses / wave speed / nonlocal hyperbolic system / communication
© EDP Sciences, 2013
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