Entropy description of a cooperation－competition system

doi:10.1088/1674-1056/19/6/061501

Abstract Understanding the cooperation--competition dynamics is a long-standing challenge in studying complex systems. Inspired by the idea of Shannon entropy, we define competition information entropy and propose an entropy evolution model. The analytic results of the model of the relation between competition gain distribution parameters and entropy, as well as the relation between entropy and time are compared with empirical results obtained in 14 real world systems. They are found to be in good agreement with each other.

Keywords: cooperation--competition entropy competition gain evolution model

Received: 21 February 2010
Revised: 12 March 2010
Accepted manuscript online:

PACS:	89.70.-a	(Information and communication theory)
	89.75.-k	(Complex systems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos.~10635040 and 70671089).

Cite this article:

Xu Xiu-Lian(徐秀莲), Fu Chun-Hua(傅春花), Liu Chun-Ping(刘春平), and He Da-Ren(何大韧) Entropy description of a cooperation－competition system 2010 Chin. Phys. B 19 060501

[1]	Bengtsson M and Kock S 2000 Industrial Marketing Management 29 411
[2]	Wang Y S and Wu H 2004 Physica A 339 609
[3]	Law R, Marrow P and Dieckmann U 1997 Evolutionary Ecology 11 485
[4]	Guimaraes Jr P R, Machado G, Aguiar M A M, Jordano P, Bascompte J, Pinheiro A and Furtado dos Reis S 2007 J. Theor. Bio. 249 181
[5]	Saavedra S, Reed-Tsochas F and Uzzi B 2009 Nature 457 463
[6]	Puurtinen M and Mappes T 2009 Proc. R. Soc. B 276 355
[7]	Pugliese E, Castellano C, Marsili M and Pietronero L 2009 Eur. Phys. J. B 67 319
[8]	Albornoz J M and Parravano A arXiv:0904.2741v2 [nlin.AO] 19 Jan 2010
[9]	Scheff\underline {r an C and Hannon B 2007 Complexity 13 78
[10]	Mohanty P K 2007 Physica A 384 75
[11]	Zhang P P, Chen K, He Y, Zhou T, Su B B, Jin Y D, Chang H, Zhou Y P, Sun L C, Wang B H and He D R 2006 Physica A 360 599
[12]	Chang H, Su B B, Zhou Y P and He D R 2007 Physica A 383 687
[13]	Zhou T, Wang B H, Jin Y D, He D R, Zhang P P, He Y, Su B B, Chen K, Zhang Z Z and Liu J G 2007 Int. J. Mod. Phys. C 18 297
[14]	Fu C H, Zhang Z P, Chang H, Tao J R, Chen Z H, Dai Y L, Zhang W and He D R 2008 Physica A 387 1411
[15]	Fu C H, Xu X L, Liu A F, Wu Y P, Shen D, Liu S J, Qian X, Feng Y C, Wei C L and He D R 2008 Chin. Phys. Lett . 25 4181
[16]	Chen Y Z, Fu C H, Chang H, Li N and He D R 2008 Chin. Phys. B 17 3580
[17]	Shi J J, Wang Y L and He D R 2009 Chin. Phys. Lett. 26 078902
[18]	Xu X L, Fu C H, Shen D, Liu A F and He D R arXiv:0910.2516v2 [physics.soc-ph]
[19]	Xu X L, Fu C H, Liu A F and He D R 2010 Chin. Phys. Lett. 27 048901
[20]	Chen H B, Fan Y, Fang J Q and Di Z R 2009 Acta Phys. Sin. 58 1383 (in Chinese)
[21]	Pickands J 1975 The Annals of Statistics 3 119
[22]	Hosking J R M and Wallis J R 1987 Technometrics 29 339
[23]	Laherrere J and Sornette D 1998 Eur. Phys. J. B 2 525
[24]	Mandelbrot B 1960 Int. Econo. Rev . 1 ({2 ) 79
[25]	Yan X Y and Wang M S 2010 Acta Phys. Sin. 59 851 (in Chinese)
[26]	Shannon C E 1948 Bell System Technical Journal 27 pp.~379--423, 623--656
[27]	Hu H B and Wang X F 2008 Physica A 387 3769
[28]	Liu S J, Qian X, Feng Y C, Fu C H, Xu X L, Liu A F, Wu Y P and He D R 2008 Review of Science &Technology 26 79 (in Chinese)

[1]	Asymmetric image encryption algorithm based ona new three-dimensional improved logistic chaotic map Guo-Dong Ye(叶国栋), Hui-Shan Wu(吴惠山), Xiao-Ling Huang(黄小玲), and Syh-Yuan Tan. Chin. Phys. B, 2023, 32(3): 030504.
[2]	Quantum properties of nonclassical states generated by an optomechanical system with catalytic quantum scissors Heng-Mei Li(李恒梅), Bao-Hua Yang(杨保华), Hong-Chun Yuan(袁洪春), and Ye-Jun Xu(许业军). Chin. Phys. B, 2023, 32(1): 014202.
[3]	Configurational entropy-induced phase transition in spinel LiMn₂O₄ Wei Hu(胡伟), Wen-Wei Luo(罗文崴), Mu-Sheng Wu(吴木生), Bo Xu(徐波), and Chu-Ying Ouyang(欧阳楚英). Chin. Phys. B, 2022, 31(9): 098202.
[4]	Robustness measurement of scale-free networks based on motif entropy Yun-Yun Yang(杨云云), Biao Feng(冯彪), Liao Zhang(张辽), Shu-Hong Xue(薛舒红), Xin-Lin Xie(谢新林), and Jian-Rong Wang(王建荣). Chin. Phys. B, 2022, 31(8): 080201.
[5]	Physical aspects of magnetized Jeffrey nanomaterial flow with irreversibility analysis Fazal Haq, Muhammad Ijaz Khan, Sami Ullah Khan, Khadijah M Abualnaja, and M A El-Shorbagy. Chin. Phys. B, 2022, 31(8): 084703.
[6]	Thermodynamic properties of two-dimensional charged spin-1/2 Fermi gases Jia-Ying Yang(杨家营), Xu Liu(刘旭), Ji-Hong Qin(秦吉红), and Huai-Ming Guo(郭怀明). Chin. Phys. B, 2022, 31(6): 060504.
[7]	Thermodynamic effects of Bardeen black hole surrounded by perfect fluid dark matter under general uncertainty principle Zhenxiong Nie(聂振雄), Yun Liu(刘芸), Juhua Chen(陈菊华), and Yongjiu Wang(王永久). Chin. Phys. B, 2022, 31(5): 050401.
[8]	A quantitative analysis method for contact force of mechanism with a clearance joint based on entropy weight and its application in a six-bar mechanism Zhen-Nan Chen(陈镇男), Meng-Bo Qian(钱孟波), Fu-Xing Sun(孙福兴), and Jia-Xuan Pan(潘佳煊). Chin. Phys. B, 2022, 31(4): 044501.
[9]	Characteristics of vapor based on complex networks in China Ai-Xia Feng(冯爱霞), Qi-Guang Wang(王启光), Shi-Xuan Zhang(张世轩), Takeshi Enomoto(榎本刚), Zhi-Qiang Gong(龚志强), Ying-Ying Hu(胡莹莹), and Guo-Lin Feng(封国林). Chin. Phys. B, 2022, 31(4): 049201.
[10]	Quantum watermarking based on threshold segmentation using quantum informational entropy Jia Luo(罗佳), Ri-Gui Zhou(周日贵), Wen-Wen Hu(胡文文), YaoChong Li(李尧翀), and Gao-Feng Luo(罗高峰). Chin. Phys. B, 2022, 31(4): 040302.
[11]	Comparison of formation and evolution of radiation-induced defects in pure Ni and Ni-Co-Fe medium-entropy alloy Lin Lang(稂林), Huiqiu Deng(邓辉球), Jiayou Tao(陶家友), Tengfei Yang(杨腾飞), Yeping Lin(林也平), and Wangyu Hu(胡望宇). Chin. Phys. B, 2022, 31(12): 126102.
[12]	Information flow between stock markets: A Koopman decomposition approach Semba Sherehe, Huiyun Wan(万慧云), Changgui Gu(顾长贵), and Huijie Yang(杨会杰). Chin. Phys. B, 2022, 31(1): 018902.
[13]	Small activation entropy bestows high-stability of nanoconfined D-mannitol Lin Cao(曹琳), Li-Jian Song(宋丽建), Ya-Ru Cao(曹亚茹), Wei Xu(许巍), Jun-Tao Huo(霍军涛), Yun-Zhuo Lv(吕云卓), and Jun-Qiang Wang(王军强). Chin. Phys. B, 2021, 30(7): 076103.
[14]	Influence of temperature and alloying elements on the threshold displacement energies in concentrated Ni-Fe-Cr alloys Shijun Zhao(赵仕俊). Chin. Phys. B, 2021, 30(5): 056111.
[15]	Identification of denatured and normal biological tissues based on compressed sensing and refined composite multi-scale fuzzy entropy during high intensity focused ultrasound treatment Shang-Qu Yan(颜上取), Han Zhang(张含), Bei Liu(刘备), Hao Tang(汤昊), and Sheng-You Qian(钱盛友). Chin. Phys. B, 2021, 30(2): 028704.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Entropy description of a cooperation－competition system

Cite this article:

Online attention