simulations of the OCR model on the network. Also, we investigate ommunities. an important issue to understand the so ial group dynami s. tisti ally signi an t frequent asso iation. The paper is organized as In this work, we deal with the problem of onsensus formation in ons. Consensus makes a position stronger, and amplies its impa t network we study was onstru ted from observation of a ommunity animal so ial network with known ommunity stru ture simulating the OCR (Opinion Changing Rate) model proposed in ref [1℄. The situations in whi h it is ne essary for a group to rea h shared de isithe inuen e of parti ular individuals in maintaining the ohesion of models. Then we des ribe a dolphin so ial network in terms of their topology from numeri al simulation of opinion dynami s models is a key aspe t of so ial group dynami s. Everyday life presents many Ties between dolphin pairs were established by observation of staon so iety. So the analysis of this so ial network under a parti ular Girvan [7℄. In the se ond part, we dis uss the results of numeri al natural divisions using betweenness-based algorithm of Newman and of 62 bottlenose dolphins living in Doubtful Sound, New Zealand [9. follow. First, we review the main features of the Kuramoto and OCR a in oherently regime. rates dened as Here is the R(t) = 1 − q N1 Pi(x˙ i(t) − X˙ (t))2. X˙ (t) average over all agents of Values of approa hing unity would x˙ i(t). R imply a high degree of opinions oheren e, while low values indi ate 4 Numeri al results of agents in ea h nal lusters.
Table 2. Distribution of agents shown in Fig. 2(a) as resulting from the simulation of OCR model over the bottlenose dolphins ommunity for Elements in parentheses represent the numbers K = 2.2. time steps in a logarithmi al s ale for the abs ise axe. 100 tend to syn hronize their a tivities due to the oupling for e (see system enters in a short unstable transient regime in whi h agents tem rapidly lusterizes resulting in two nal lusters in whi h agents the de ision hanging rate and the order parameter overs (x˙ (t)) R(t) ea h nal lusters is reported in Table 2. order parameter (see Fig. 2(b)). Immediately after, the sys- R(t) values. The results are presented in Fig. 2. Panels (a) and (b) show Fig. 2(a)). This regime is hara terized by maximum values of the in the initial state all dolphins share the same de ision hanging rate present in bottlenose dolphins so iety. The distribution of agents in As it an be appre iated, as soon as we start the simulation, the share ommon d r values. This situation ree t ommunity stru ture 10−1 (b) 100 101 102 from the simulation of OCR model over the bottlenose dolphins ommunity for and K = 2.2 ω(2) = 0.
Table 3. Distribution of agents shown in Fig. 3(a) as resulting als with high absolute value of and ω: ω(29) = 0.41 ω(48) = −0.47. The rst one is when this entral agent have natural de ision For this split into 4 lusters, the modularity is Details Q = 0.3822. hanging rate set to zero value simulating a exible agent. (ω(2) ≃ 0) Results are shown in Fig. 3. As it an be appre iated, two new single of that Distribution of agents is reported in Table 3. groups formed by verti es 29 and 48 merge. It orrespond to individu0.5 0.4 ) 0.3 r (cd0.2 e t ra0.1 g n ign 0 a ch−0.1 n o i isc−0.2 e d−0.3 −0.4 −0.5 r 1 e t e rm0.9 a a p r0.8 e d rO0.7 10−2 network. On the other hand, the natural de ision hanging rate of entral individuals is determinate in lusters formation pro ess.