Vol. No. Jan. 96, Effects of Internal Dynamics and Micro-Macro Loop on Dynamics of Social Structures Takashi Sato, and Takashi Hashimoto We discuss a condition required for forming and maintaining dynamics of macro structure in a society from the dynamical view of society, which regards social structure as dynamically changing with time. We summarize results of a multi-agent simulation composed of agents having internal dynamics. In the simulation, we observe the dynamics of a macro structure itinerating among various kinds of ordered patterns via aperiodic motion. Further, we report results of analyses investigating an effect of the micro-macro loop on dynamics of social structures. Based on the analyses, we conclude that internal dynamics of agents and micro-macro loop are necessary to form and maintain an endogenous dynamics of social structure.. / 2),2) School of Knowledge Science, Japan Advanced Institute of Science and Technology Presently with Initial Research Project, Okinawa Institute of Science and Technology, JST Blumer 2) Tarde / 25) Veblen 29) / /
2 Jan. 96 Simon 22) Knight 4) Hayek 9) voluntarism 24) 5) 8) ) Simple Recurrent Network with Self-Influential Connection; SRN-SIC SRN-SIC 9) SRN-SIC circadian rhythm Necker Cube Varela 28) Karmiloff-Smith 3) Gelder Gelder 26),27) / Necker Cube 6),8)
Vol. No. 3 ),2) 2 SRN-SIC SRN-SIC 9) / 2 SRN-SIC 3 / 4 / 5 2. 2. / 2.2 Elman Simple Recurrent Network; SRN 6) SRN SRN with Self-Influential Connection; SRN-SIC 9) SRN 2 Necker Cube 2 7),23) Giddens 7)
4 Jan. 96 Own past output value Output Layer L Hidden Layer L Input Layer L L External Stimulus : Unlearnable (Weights are fixed at.) : Learnable (By normal BP) Context Layer Hidden neurons past output values SRN SRN-SIC Fig. Architecture of agent having internal dynamics, called Simple Recurrent Network with Self- Influential Connection (SRN-SIC). 4 SRN-SIC SRN-SIC SRN-SIC -.. () L(net) =tanh(βnet) () net β L SRN-SIC (2) (3) o k (t) =L(net k (t)) (2) net k (t) = w kj v j(t)+θ k (3) j o k (t) t k w kj k j v j(t) t j θ k k (4) (5) v j(t) =L(net j(t)) (4) net j(t) = w jix i(t)+ w jh v h (t ) i h + w jl o l (t ) + θ j (5) l w ji j i x i(t) t i w jh j h v h (t ) t h w jl j l o l (t ) t l θ j j SRN-SIC. SRN-SIC 2.3 Challet Minority Game MG 3) MG 3) MG 2 MG () n 2 or - or (2) SRN-SIC -.. MG. -
Vol. No. 5 MG MG - or,, SRN-SIC SRN-SIC 5 2 SRN-SIC. SRN-SIC -.5.5. MG,,,.. 2 2 3 3 3 3 ) 2) 3) 4) 5) 6) 6 9) - 2 )
6 Jan. 96.. 284.. 2845 284 2846 2842 2847 2843 2848 2844 2849 2845 285 Fig. 2 2 An example of the itinerant dynamics at the macro level in one turn. Table Classification of dynamics observed at the macro level in one turn. 2 ( ) Veblen 3) Veblen 5) Veblen 4 Challet MG 3) 4),5) MG MG
Vol. No. 7 MG 3. 3. 2 / 28, 29, 28 28,,, 28,,28, 28 78,,, ) -... 2) 2 3(a) (c) -... 3(a) (c) 3(a) (c) 4 a -.. b -.5.5 c -.. 4 a c 4 a c 3.2 28 2 5 a 5 b
8 Jan. 96 (a) -. is given. Start 7798 7799 78 78 782 9998 9999 e+6.e+6.2e+6 (b). is given. Start 7798 7799 78 78 782 9998 9999 e+6.e+6.2e+6 Start 7798 7799 78 78 782 3 Fig. 3 (c). is given. 9998 9999 e+6.e+6.2e+6 Collapse and regeneration of the itinerant dynamics by starting and ending of the artifactual fixed inputs. (a) Random number between -. and. is given. Start 7798 7799 78 78 782 9998 9999 e+6.e+6.2e+6 (b) Random number between -.5 and.5 is given. Start 7798 7799 78 78 782 9998 9999 e+6.e+6.2e+6 (c) Random number between -. and. is given. Start 7798 7799 78 78 782 9998 9999 e+6.e+6.2e+6 4 Fig. 4 Collapse and regeneration of the itinerant dynamics by starting and ending of the uniform random inputs with various ranges. 5 a b a 4 b
Vol. No. 9 (a) Different itinerant dynamics is shaped. 42 44 46 48 5 52 (b) Intermittent dynamics is shaped. Regenerated the original period four dynamics Regenerated the original fixed point 842 844 846 848 85 852 5 a b Fig. 5 Dynamics at the macro level when the itinerant dynamics is input to the agents shaping (a) single fixed and (b) single periodic dynamics. 4. 2 2 Table 2 Summary of the experiments in which the micromacro loop is temporarily cut off. 3 3 2 3
Jan. 96 3 Table 3 The correspondence between dynamics at the macro level and the configuration of agents at the micro level. Hidden_4.5 -.5 -.5 - -.5 Output.5 - -.5 Hidden_3 6 Fig. 6 The strategy of agent showing chaotic behavior in the group shaping the itinerant dynamics. 9 6 3 3 x y z 3 4 3 6 3 5. (SRN-SIC)
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