82 research outputs found

    Transitional dynamics of the invading scenario.

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    <p>We set two gradients for parameter <i>p<sub>c_ii</sub></i>: 0.075 and 0.125; while other parameters are kept constant (<i>n</i><sub>o</sub>β€Š=β€Š<i>n</i><sub>i</sub>β€Š=β€Š100, <i>p<sub>c_oo</sub></i>β€Š=β€Š0.1, <i>a/b</i>β€Š=β€Š100, <i>p<sub>m</sub></i>β€Š=β€Š0.01). The mean and standard deviation of total productivity and number of occupations of the original society (<i>So</i>) and invader society (<i>Si</i>) are shown. In the first situation, the invader society is not as competent as the original society, and thus the original society is not affected; while in the second situation, the invading society is more competent, causes the extinction of the original society.</p

    Structure of virtual society, which could be represented by a graph composed of all the occupations of the society as nodes and interactions between them as edges.

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    <p>By our definition, each occupation in the society is supported (directly or mediated by other occupations) by each other occupation in the society, <i>i.e.</i>, the graph should be irreducible to denote the structure of a legal society (this does not applies to derived society). Solid arrows in the figure denote supporting relationships. A, B, C are irreducible graphs, and thus represent legal society, while D, E, F, G are not. For D, the two occupations are not connected; for E, occupation 1 is not supported; for F, occupation 4 doesn't support other occupations; for G, occupation 5 and 6 do not support other occupations.</p

    Simulating Society Transitions: Standstill, Collapse and Growth in an Evolving Network Model

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    <div><p>We developed a model society composed of various occupations that interact with each other and the environment, with the capability of simulating three widely recognized societal transition patterns: standstill, collapse and growth, which are important compositions of society evolving dynamics. Each occupation is equipped with a number of inhabitants that may randomly flow to other occupations, during which process new occupations may be created and then interact with existing ones. Total population of society is associated with productivity, which is determined by the structure and volume of the society. We ran the model under scenarios such as parasitism, environment fluctuation and invasion, which correspond to different driving forces of societal transition, and obtained reasonable simulation results. This work adds to our understanding of societal evolving dynamics as well as provides theoretical clues to sustainable development.</p></div

    Transitional dynamics of the disturbing scenario.

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    <p>We set three gradients for parameter <i>r<sub>d</sub></i>: 4, 10 and 25, while other parameters are kept constant (<i>n</i><sub>o</sub>β€Š=β€Š<i>n<sub>d</sub></i>β€Š=β€Š100, <i>p<sub>c_oo</sub></i>β€Š=β€Š0.1, <i>a/b</i>β€Š=β€Š100, <i>p<sub>m</sub></i>β€Š=β€Š0.01). 50 replications are run for each combination. It could be revealed as <i>r<sub>d</sub></i> increases, more productivity and occupations would be lost in the fluctuation, and more time needed for recovering. The society also suffers a greater risk of being wiped out when <i>r<sub>d</sub></i> gets larger. In the condition that <i>r<sub>d</sub></i> β€Š=β€Š25, 5 out of the 50 replications resulted in the extinction of the society, while none happened in the other two conditions.</p

    Transitional dynamics of the mutually supporting scenario.

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    <p>The original society and the derived society are mutually supportive, they compose a new society, which could be interpreted as growing of the original society. Situation 1: <i>p<sub>c_od</sub></i>β€Š=β€Š <i>p<sub>c_do</sub></i>β€Š=β€Š <i>p<sub>c_dd</sub></i>β€Š=β€Š0.5, situation 2: <i>p<sub>c_od</sub></i>β€Š=β€Š <i>p<sub>c_do</sub></i>β€Š=β€Š <i>p<sub>c_dd</sub></i>β€Š=β€Š1.5. Other parameters are kept constant (<i>n<sub>o</sub></i>β€Š=β€Š<i>n<sub>d</sub></i>β€Š=β€Š100, <i>p<sub>c_oo</sub></i>β€Š=β€Š0.1, <i>a/b</i>β€Š=β€Š100, <i>p<sub>m</sub></i>β€Š=β€Š0.01). The mean and standard deviation of total productivity and number of occupations of the original (<i>So</i>), derived (<i>Sd</i>) and merged society(<i>Sm</i>) are shown. Productivity of the occupations of the original society could decrease (situation 1) or increase (situation 2) during the growing process due to different supporting strength.</p

    Evolving dynamics of a model society.

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    <p>We set <i>n</i> to 100, while <i>a/b</i>, <i>p<sub>c</sub></i>, and <i>p<sub>m</sub></i>, are assigned two optional values each, which are: <i>a/b</i>1β€Š=β€Š60, <i>a/b</i>2β€Š=β€Š120; <i>p<sub>c</sub></i>1β€Š=β€Š0.1, <i>p<sub>c</sub></i>2β€Š=β€Š0.4; <i>p<sub>m</sub></i>1β€Š=β€Š0.01, <i>p<sub>m</sub></i>2β€Š=β€Š0.04. All of the 8 combinations of these parameter values are used for the simulation, and each combination is run with 50 replications. The mean and standard deviation of total productivity and number of occupations of the society are shown. Each combination is termed with four numbers in the figure label, (<i>e.g.</i>, 111 refers to the parameter combination β€œ<i>a/b</i>1, <i>p<sub>c</sub></i>1, <i>p<sub>m</sub></i>1”, while 221 refers to the combination β€œ<i>a/b</i>2, <i>p<sub>c</sub></i>2, <i>p<sub>m</sub></i>1”, <i>etc</i>). The 4 final productivity values revealed in the figure correspond to the 4 different combinations of <i>a/b</i> and <i>p<sub>c</sub></i>, while for each of these combinations, the larger <i>p<sub>m</sub></i> value corresponds with the short transition time.</p

    Distribution of steady state productivity.

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    <p>(A) Productivity distribution of the parameter combination 211 as an example. Mean value is used for plotting while standard deviation is represented with error bars. (B) Result of Shapiro-Wilk normality test of productivity distribution of occupations at steady state. All 50 replications of the 8 situations are tested, mean and standard deviation of W statistics and P-value are shown.</p

    Transitional dynamics of the supporting scenario.

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    <p>We set three different combinations of parameter values: (1) <i>n<sub>d</sub></i>β€Š=β€Š50, <i>p<sub>c_od</sub></i>β€Š=β€Š0.1<sub>, </sub><i>p<sub>c_dd</sub></i>β€Š=β€Š0; (2) <i>n<sub>d</sub></i>β€Š=β€Š200, <i>p<sub>c_od</sub>β€Š=β€Š</i>0.2<sub>, </sub><i>p<sub>c_dd</sub></i>β€Š=β€Š0; (3) <i>n<sub>d</sub></i>β€Š=β€Š200, <i>p<sub>c_od</sub>β€Š=β€Š</i>0.2<sub>, </sub><i>p<sub>c_dd</sub></i>β€Š=β€Š0.05; while other parameters are kept constant (<i>n</i><sub>o</sub>β€Š=β€Š<i>n<sub>d</sub></i>β€Š=β€Š100, <i>p<sub>c_oo</sub></i>β€Š=β€Š0.1, <i>a/b</i>β€Š=β€Š100, <i>p<sub>m</sub></i>β€Š=β€Š0.01). For each combination, 50 replications are run, and the mean and standard deviation of total productivity and number of occupations of the original society (<i>So</i>) and derived society (<i>Sd</i>) are shown. In combination 1, <i>So</i> is affordable of <i>Sd</i> that parasitize it thus result in the coexistence of <i>So</i> and <i>Sd</i>. In combination 2, <i>Sd</i> has a much larger size (<i>n<sub>d</sub></i>) and the parasitism efficiency is also improved (<i>p<sub>c_od</sub></i>), thus <i>So</i>’s number of occupation and productivity are greatly shrinked; in 4 of the 50 replications, <i>So</i> is completely eliminated. As a result, <i>Sd</i> also suffers a big drop of its productivity and number of occupations, or even goes extinct in the conditions that <i>So</i> is completely ruined. In combination 3, <i>Sd</i> is able to support itself, thus more competent in grabbing the productivity contributed by <i>So</i>; besides, it is able to survive after <i>So</i>’s collapse, thus result in the replacing of <i>So</i> by <i>Sd</i>. The productivity of <i>Sd</i> undergoes a short dropping before it rise again to steady value, that is because as <i>So</i> quickly collapses, its supporting to <i>Sd</i> is deprived.</p

    Relationships between two societies.

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    <p>(A) Competition between S1 and S2. (B) S1 supports S2. (C) Mutually supporting between S1 and S2. (D) S1 invades S2.</p

    Model parameters.

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    <p>Model parameters.</p
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