{"title":"Synchronization of Chaos in a Food Web in Ecological Systems","authors":"Anuraj Singh, Sunita Gakkhar","volume":45,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1247,"pagesEnd":1252,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/14852","abstract":"
The three-species food web model proposed and investigated by Gakkhar and Naji is known to have chaotic behaviour for a choice of parameters. An attempt has been made to synchronize the chaos in the model using bidirectional coupling. Numerical simulations are presented to demonstrate the effectiveness and feasibility of the analytical results. Numerical results show that for higher value of coupling strength, chaotic synchronization is achieved. Chaos can be controlled to achieve stable synchronization in natural systems.<\/p>\r\n","references":"[1] M. A. Aziz-Alaoui, \"Synchronization of Chaos\", Encyclopedia of\r\nmathematical physics, 2006.\r\n[2] A. Pikovsky, M. Rosenblum and J. Kurths, Synchronization: A\r\nuniversal Concept in Nonlinear Science. Cambridge: Cambridge\r\nUniversity Press..\r\n[3] L. Pecora and T. Carroll, \"Synchronization in chaotic systems,\"\r\nPhysics Review Letters, vol. 64, No. 8, pp. 821-824, 1990.\r\n[4] S. Gakkhar and R. K. Naji, \"Order and chaos in a food web\r\nconsisting of a predator and two Independent preys,\"\r\nCommunications in Nonlinear Science and Numerical Simulation,\r\nvol. 10, pp. 105-120, 2005.\r\n[5] X.J. Wu, J. Lie and R. K. Upadhayay, \"Chaos control and\r\nsynchronization of a three-species food chain model via Holling\r\nfunctional response,\" International Journal of Computer\r\nMathematics, pp.1- 16, 2008.\r\n[6] A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano,\r\n\"Determining Lyapunov exponents from a time series,\" Physica D,\r\nvol. 16, pp. 285-317, 1985.\r\n[7] J. L. Kaplan and J. Yorke, \"Chaotic behaviour of multidimensional\r\ndifference equations\", Functional Differential Equations and\r\nApproximations of Fixed points, edited by H. O. Walter and H-O.\r\nPeitgen, vol. 730 of Lectures Notes in Mathematics, Springer,\r\nBerlin, 1979, pp. 204-227.\r\n[8] L. Pecora and T. Carroll, \"Master Stability Functions for\r\nSynchronized Coupled System,\" Physics Review Letters, vol. 64,\r\nno. 8, pp. 821-824, 1990.\r\n[9] J. Heagy, L. Pecora and T. Carroll, \"Short wavelength Bifurcations\r\nand Size instabilities in Coupled Oscillator Systems,\" Physical\r\nReview Letters, vol. 74, no. 21, pp. 4185-4188, 1995.\r\n[10] J. Heagy, T. Carroll, and L. Pecora, \"Synchronous Chaos in Coupled\r\nOscillator Systems,\" Physical Review E, vol. 50, no. 3, pp. 1874-\r\n1884, 1994.\r\n[11] G. Chen and X. Dong, From Chaos to Order, Singapore: World\r\nScientific, 1998.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 45, 2010"}