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Program and Abstract of Talks Morning, May 16 Time Room/Chair 8:00-8:30 Room A Opening Ceremony Speech by President Maoan Han Speech by Peter Bates Speech by Jianshe Yu 8:30-8:40 Group Photo Time Room/Chair Speaker Room/Chair Speaker Room A Room B 8:40-9:20 Peter Bates Qiru Wang 9:20-10:00 Kening Lu Chongqing Cheng Pei Yu Xilin Fu 10:00-10:20 Coffee/Tea Break Room A Room B 10:20-11:00 Pei Yu Michael Li 11:00-11:40 Valery Romanovskii Wenxin Qin Yuncheng You Meng Fan 11:40-12:00 Regilene D. S. Oliveira Chuncheng Wang 12:00-14:00 Lunch Break Afternoon, May 16 Time Room/Chair Speaker Room/Chair Speaker Room A Room B 14:00-14:40 Xiaobiao Lin Zengji Du 14:40-15:20 Hans-Otto Walther Wenzhang Huang Zhaosheng Feng Xiaoying Han 15:20-16:00 Peixuan Weng Qingjie Cao 16:00-16:20 Coffee/Tea Break Room A Room B 16:20-17:00 Zhen Jin Jianhua Shen 17:00-17:40 Wenzhang Huang Xiaojie Hou Xiaobiao Lin Xinchu Fu 17:40-18:00 Jian Fang Xu Zhang 18:10 Dinner Morning, May 17 Time Room/Chair Speaker Room/Chair Speaker Room A Room B 8:00-8:40 Kening Lu Zhaosheng Feng 8:40-9:20 Peter Bates Dongmei Xiao Jia Li Wei Ding 9:20-10:00 Huyi Hu Xiaosong Yang 10:00-10:20 Coffee/Tea Break Room A Room B 10:20-11:00 Yongluo Cao Yi Wang 11:00-11:40 Huyi Hu Wen Huang Daoyi Xu Fengjuan Chen 11:40-12:00 Yepeng Xing Kanat Shakenov 12:00-14:00 Lunch Break Afternoon, May 17 Time Room/Chair Speaker Room/Chair Speaker Room A Room B 14:00-14:40 Jia Li Valery Romanovskii 14:40-15:20 Huaiping Zhu Jifa Jiang Dongmei Xiao Xiang Zhang 15:20-16:00 Lin Wang Yuming Shi 16:00-16:20 Coffee/Tea Break Room A Room B 16:20-17:00 Huaiping Zhu Yulin Zhao 17:00-17:40 Xingfu Zou Yun Kang Xiang Zhang Dingbian Qian 17:40-18:00 Ying Su Simon Serovaisky 18:10 Banquet Morning, May 18 Time Room/Chair Speaker Room/Chair Speaker Room A Room B 8:00-8:40 Hans-Otto Walther Daoyi Xu 8:40-9:20 Jianshe Yu Xingfu Zou Maoxun Tang Ruyun Ma 9:20-10:00 Junping Shi Xiaohua Zhao 10:00-10:20 Tea Break Room A Room B 10:20-11:00 Jianshe Yu Fengxin Chen 11:00-11:40 Junjie Wei Moxun Tang Ruyun Ma Shangjiang Guo 11:40-12:00 Jinfeng Wang Changjian Liu 12:00-14:00 Lunch Break Afternoon, May 18 Time Room/Chair Speaker Room/Chair Speaker Room A Room B 14:00-14:40 Weinian Li Tiancheng Ouyang 14:40-15:20 Fengxin Chen Yuncheng You Junping Shi Weihua Jiang 15:20-16:00 Shengfan Zhou Weiming Wang 16:00-16:20 Coffee/Tea Break Room A Room B 16:20-17:00 Yi Li Maoan Han 17:00-17:20 Tiancheng Ouyang Shiliang Wu Michael Li Indranil SenGupta 17:20-17:40 Jianxin Liu Minghui Qi 18:10 Dinner Abstract of Talks In the multiple authors case, the name with ∗ is the speaker. 1. Heirarchy of solutions to gradient elliptic systems with symmetry Peter W. Bates Department of Mathematics, Michigan State University East Lansing, MI 48824, USA Email: [email protected] Abstract: (Preliminary report) We examine the asymptotic states of symmetric solutions to n n ∆u−grad W (u) = 0, u : R ! R constructed by Alikakos and Fusco. Here W is equivariant under a finite reflection group and has n + 1 nondegenerate minima. Passing to the limit as x ! 1 in certain direction gives lower dimensional solutions with symmetry. This is joint work with N. Alikakos. 2. Periodic Solutions of the Perturbed SD Oscillator Qingjie Cao*, Zhixin Li, Yushu Chen, Marian Wiercigroch Centre for Nonlinear Dynamics Research, School of Astronautics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, P.R. China Email: [email protected] Abstract: An oscillator with strong irrational nonlinearities, or a smooth and discontinuous (SD) oscillator was proposed and investigated by Cao et al. [1, 2, 3], previously, which allows one to study the transition from smooth to discontinuous dynamics depending on the value of the smoothness parameter α. In this paper, we investigate the perturbed periodic motions near the hyperbolic and non-hyperbolic equilibria of SD Oscillator. Averaging technique is introduced to this strongly nonlinear system and the responses to both the external frequency and the amplitude are derived. The results presented in this paper are valid for both smooth and discontinuous regimes of the system. References [1] Q. Cao, M. Wiercigroch, E. E. Pavlovskaia, C. Grebogi, J.M.T. Thompson, Archetypal oscillator for smooth and discontinuous dynamics, Physical Review E 74(4), 046218, 2006. [2] Q. Cao, M. Wiercigroch, E. E. Pavlovskaia, C. Grebogi, J.M.T. Thompson, Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics, Phi. Tran. Roy. Soc. A, 366(1865), 635-652, 2008. [3] Q. Cao, M. Wiercigroch, E. E. Pavlovskaia, C. Grebogi, J.M.T. Thompson, The limit case response of the archetypal oscillator for smooth and discontinuous dynamics, Inter. J. Non. Mech. 43, pp. 462{473, 2008. 1 3. Dimension estimate and multifractal analysis of C1 average conformal repeller Yongluo Cao Department of Mathematics, Soochow University, Suzhou 215006, Jiangsu, P.R.China. Email: [email protected] Abstract: In this talk, C1 average conformal repeller is considered. We give a direct proof of dimension formula of C1 average conformal repeller and we also consider pointwise dimension of invariant measure. Furthermore, we consider multifractal analysis of Lyapunov spectrum of asymptotically additive potential for C1 average conformal repeller. 4. Heteroclinic tangles in time-periodic equations Fengjuan Chen Center of Dynamical System and Nonlinear Sciences, Department of Mathematics, Zhejiang Normal University Jinhua, Zhejiang, 321004, P.R. China Email: [email protected] Abstract: This is a study on periodically perturbed second order differential equations with dissipation. We prove that, when a heteroclinic loop is periodically perturbed, three types of heteroclinic tangles are created and they compete in the space of perturbed parameters. The three types are (a) transient heteroclini tangles admitting no physical measures; (b) heteroclinic tangles for which the only physical measures admitted are sinks representing stable dynamical behavior; and (c) heteroclinic tangles with strange attractors admitting SRB measures representing chaos. We also prove that the organization of the three types of heteroclinic tangles depends sensitively on the ratio of the unstable eigenvalues of the saddle fixed points of the heteroclinic connections. The theory developed in this paper is explicitly applicable to the analysis of a given set of differential equations and the results obtained are well beyond the capacity of the classical Birkhoff-Melnikov-Smale method. This is a joint work with Maoan Han and Jibin Li. 5. Genetic Diversity and Anderson Localization Fengxin Chen Department of Mathematics, University of Texas at San Antonio San Antonio, TX 78249 Email: [email protected] Abstract: Models for genotype diversity are analyzed. It is proved that the long time behavior of a class of genotype evolution models is governed by the principal eigenvectors 2 of sum of mutation and fitness matrices. It is proved that the components of principal eigenvectors are symmetric and monotonically decreasing in terms of Hamming distances. Anderson localization is compared to understand the genotype diversity. 6. Non-existence of KAM torus Chong Qing Cheng Department of Mathematics, Nanjing University Nanjing, Jiangsu 210093, P.R.China Email: [email protected] Abstract: Given an integrable Hamiltonian h0 with n-degrees of freedom and a Diophantine r frequency !, then, arbitrarily close to h0 in the C topology with r < 2n, there exists an analytical Hamiltonian h such that the Hamiltonian flow Φt does not admit the KAM torus h with rotation vector !. In contrast with it, KAM tori exist if perturbations are small in Cr topology with r > 2n. 7. Synchronization for fuzzy cellular neural networks Wei Ding School of Mathematical Sciences, Shanghai Normal University, Shanghai, P.R. China Email: [email protected] Abstract: In this letter, the synchronization schemes for delayed fuzzy cellular neural net- works is considered. Based on the simple adaptive controller, a set of sufficient conditions to guarantee the synchronization are obtained. Moreover, the asymptotic behavior of the unknown parameters can be derived in the meanwhile. At last, some examples and their simulations are given to show the effectiveness of the main results. 8. Existence and Global Attractivity of Positive Periodic Solution to a Lotka-Volterra Model Zengji Du School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, Jiangsu 221116, P.R. China Email: [email protected] Abstract: In this paper, by using Mawhin's continuation theorem and constructing suitable Lyapunov functional, a Lotka-Volterra model with mutual interference and Holling type III functional response is studied. Some sufficient conditions are obtained for the existence, uniqueness and global attractivity of positive periodic solution of the model. Furthermore, the conditions are related to the interference constant m. Keywords Global attractivity; Mawhin's construction theorem; Positive periodic solution; Lyapunov functional; Holling type III functional response. 3 9. Global asymptotic stability for predator-prey systems whose prey receives time-variation of the environment Meng Fan School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, 130024, P.R. China Email: [email protected] Abstract: A predator-prey model with prey receiving time-variation of the environment is considered. Such a system is shown to have a unique interior equilibrium that is globally asymptotically stable if the time-variation is bounded and weakly integrally positive.
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