{"id":18,"date":"2016-09-05T00:30:19","date_gmt":"2016-09-05T04:30:19","guid":{"rendered":"https:\/\/sciencescosmaincms.cm.ucf.edu\/math\/zshuai\/?page_id=18"},"modified":"2016-09-05T00:30:34","modified_gmt":"2016-09-05T04:30:34","slug":"graph","status":"publish","type":"page","link":"https:\/\/sciences.ucf.edu\/math\/zshuai\/graph\/","title":{"rendered":"Graph-Theoretic Approach"},"content":{"rendered":"<p>A Graph-Theoretic Approach to the Construction of Lyapunov Functions for Large-Scale Differential Equation Systems<br \/>\n<cite>\u00a0\u00a0* Please contact me via email (<a href=\"mailto:shuai@ucf.edu\">shuai@ucf.edu<\/a>) to add\/remove a paper from this list<\/cite><\/p>\n<hr \/>\n<p><strong>Theoretical Development on the Graph-Theoretic Approach<\/strong><\/p>\n<ul>\n<li>H. Guo, M.Y. Li, Z. Shuai.<br \/>\n<cite>Global stability of the endemic equilibrium of multigroup SIR epidemic models<\/cite>.<br \/>\nCanadian Applied Mathematics Quarterly, 14 (2006) 259-284. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2006camq.pdf\">pdf<\/a><\/strong><\/li>\n<li>H. Guo, M.Y. Li, Z. Shuai.<br \/>\n<cite>A graph-theoretic approach to the method of global Lyapunov functions<\/cite>.<br \/>\nProceedings of the American Mathematical Society, 136 (2008) 2793-2802. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2008pams.pdf\">pdf<\/a><\/strong><\/li>\n<li>M.Y. Li, Z. Shuai.<br \/>\n<cite>Global-stability problem for coupled systems of differential equations on networks<\/cite>.<br \/>\nJournal of Differential Equations, 248 (2010) 1-20. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2010jde.pdf\">pdf<\/a><\/strong><\/li>\n<li>Z. Shuai, P. van den Drissche.<br \/>\n<cite>Global stability of infectious disease models using Lyapunov functions<\/cite>.<br \/>\nSIAM Journal on Applied Mathematics, 73 (2013) 1513-1532. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2013siap.pdf\">pdf<\/a><\/strong><\/li>\n<\/ul>\n<p><strong>Application of the Graph-Theoretic Approach<\/strong><\/p>\n<ul>\n<li>Y. Xiao, X. Zou.<br \/>\n<cite>Global stability in a model for interactions between two strains of host and one strain of parasite<\/cite>.<br \/>\nCanadian Applied Mathematics Quarterly, 16 (2008) 211-218.<\/li>\n<li>M.Y. Li, Z. Shuai.<br \/>\n<cite>Global stability of an epidemic model in a patchy environment<\/cite>.<br \/>\nCanadian Applied Mathematics Quarterly, 17 (2009) 175-187. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2009camq.pdf\">pdf<\/a><\/strong><\/li>\n<li>M.Y. Li, Z. Shuai, C. Wang.<br \/>\n<cite>Global stability of multi-group epidemic models with distributed delays<\/cite>.<br \/>\nJournal of Mathematical Analysis and Applications, 361 (2010) 38-47. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2010jmaa.pdf\">pdf<\/a><\/strong><\/li>\n<li>Z. Yuan, L. Wang.<br \/>\n<cite>Global stability of epidemiological models with group mixing and nonlinear incidence rates<\/cite>.<br \/>\nNonlinear Analysis: Real World Applications, 11 (2010) 995-1004.<\/li>\n<li>R. Sun.<br \/>\n<cite>Global stability of the endemic equilibrium of multigroup SIR models with nonlinear incidence<\/cite>.<br \/>\nComputers &amp; Mathematics with Applications, 60 (2010) 2286-2291.<\/li>\n<li>Z. Yuan, X. Zou.<br \/>\n<cite>Global threshold property in an epidemic model for disease with latency spreading in a heterogeneous host population<\/cite>.<br \/>\nNonlinear Analysis: Real World Applications, 11 (2010) 3479-3490.<\/li>\n<li>Z. Shuai, P. van den Driessche.<br \/>\n<cite>Global dynamics of cholera models with differential infectivity<\/cite>.<br \/>\nMathematical Biosciences, 234 (2011) 118-126. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2011mbs.pdf\">pdf<\/a><\/strong><\/li>\n<li>C. Ji, D. Jiang, N. Shi.<br \/>\n<cite>Multigroup SIR epidemic model with stochastic perturbation<\/cite>.<br \/>\nPhysica A: Statistical Mechanics and its Applications, 390 (2011) 1747-1762.<\/li>\n<li>G. Rozhnova, A. Nunes, A.J. McKane.<br \/>\n<cite>Stochastic oscillations in models of epidemics on a network of cities<\/cite>.<br \/>\nPhysical Review E, 84 (2011) 051919.<\/li>\n<li>R. Sun, J. Shi.<br \/>\n<cite>Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates<\/cite>.<br \/>\nApplied Mathematics and Computation, 218 (2011) 280-286.<\/li>\n<li>H. Chen, J. Sun.<br \/>\n<cite>Global stability of delay multigroup epidemic models with group mixing and nonlinear incidence rates<\/cite>.<br \/>\nApplied Mathematics and computation, 218 (2011) 4391-4400.<\/li>\n<li>T. Kuniya.<br \/>\n<cite>Global stability analysis with a discretization approach for an age-structured multigroup SIR epidemic model<\/cite>.<br \/>\nNonlinear Analysis: Real World Applications, 12 (2011) 2640-2655.<\/li>\n<li>D. Ding, X. Ding.<br \/>\n<cite>Global stability of multi-group vaccination epidemic models with delays<\/cite>.<br \/>\nNonlinear Analysis: Real World Applications, 12 (2011) 1991-1997.<\/li>\n<li>Z. Shuai, P. van den Driessche.<br \/>\n<cite>Impact of heterogeneity on the dynamics of an SEIR epidemic model<\/cite>.<br \/>\nMathematical Biosciences and Engineering, 9 (2012) 393-411. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2012mbe.pdf\">pdf<\/a><\/strong><\/li>\n<li>H. Guo, M.Y. Li, Z. Shuai.<br \/>\n<cite>Global dynamics of a general class of multi-stage models for infectious diseases<\/cite>.<br \/>\nSIAM Journal on Applied Mathematics, 72 (2012) 261-279. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2012siap.pdf\">pdf<\/a><\/strong><\/li>\n<li>H. Guo, M.Y. Li.<br \/>\n<cite>Impacts of migration and immigration on disease transmission dynamics in heterogeneous populations<\/cite>.<br \/>\nDiscrete and Continuous Dynamical Systems Series B, 17 (2012) 2413-2430.<\/li>\n<li>C. Ji, D. Jiang, Q. Yang, N. Shi.<br \/>\n<cite>Dynamics of a multigroup SIR epidemic model with stochastic perturbation<\/cite>.<br \/>\nAutomatica, 48 (2012) 121-131.<\/li>\n<li>K. Li, Z. Ma, Z. Jia, M. Small, X. Fu.<br \/>\n<cite>Interplay between collective behavior and spreading dynamics on complex networks<\/cite>.<br \/>\nChaos: An Interdisciplinary Journal of Nonlinear Science, 22 (2012) 043113.<\/li>\n<li>H. Su, W. Li, K. Wang.<br \/>\n<cite>Global stability analysis of discrete-time coupled systems on networks and its applications<\/cite>.<br \/>\nChaos: An Interdisciplinary Journal of Nonlinear Science, 22 (2012) 033135.<\/li>\n<li>H. Shu, D. Fan, J. Wei.<br \/>\n<cite>Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission<\/cite>.<br \/>\nNonlinear Analysis: Real World Applications, 13 (2012) 1581-1592.<\/li>\n<li>T. Kajiwara, T. Sasaki, Y. Takeuchi.<br \/>\n<cite>Construction of Lyapunov functionals for delay differential equations in virology and epidemiology<\/cite>.<br \/>\nNonlinear Analysis: Real World Applications, 13 (2012) 1802-1826.<\/li>\n<li>W. Li, L. Pang, H. Su, K. Wang.<br \/>\n<cite>Global stability for discrete Cohen\u00d0Grossberg neural networks with finite and infinite delays<\/cite>.<br \/>\nApplied Mathematics Letters, 25 (2012) 2246-2251.<\/li>\n<li>W. Li, H. Su, D. Wei, K. Wang.<br \/>\n<cite>Global stability of coupled nonlinear systems with Markovian switching<\/cite>.<br \/>\nCommunications in Nonlinear Science and Numerical Simulation, 17 (2012) 2609-2616.<\/li>\n<li>C. Yuan, D. Jiang, D. O&#8217;Regan, R.P. Agarwal.<br \/>\n<cite>Stochastically asymptotically stability of the multi-group SEIR and SIR models with random perturbation<\/cite>.<br \/>\nCommunications in Nonlinear Science and Numerical Simulation, 17 (2012) 2501-2516.<\/li>\n<li>J. Wang, J. Zu, X. Liu, G. Huang, J. Zhang.<br \/>\n<cite>Global dynamics of a multi-group epidemic model with general relapse distribution and nonlinear incidence rate<\/cite>.<br \/>\nJournal of Biological Systems, 20 (2012) 235-258.<\/li>\n<li>J. Wang, Y. Takeuchi, S. Liu.<br \/>\n<cite>A multi-group SVEIR epidemic model with distributed delay and vaccination<\/cite>.<br \/>\nInternational Journal of Biomathematics, 5 (2012) No. 3.<\/li>\n<li>D. Ding, X. Wang, X. Ding.<br \/>\n<cite>Global stability of multigroup dengue disease transmission model<\/cite>.<br \/>\nJournal of Applied Mathematics, 2012 (2012) 342472.<\/li>\n<li>M.C. Eisenberg, Z. Shuai, J.H. Tien, P. van den Driessche.<br \/>\n<cite>A cholera model in a patchy environment with water and human movement<\/cite>.<br \/>\nMathematical Biosciences, 246 (2013) 105-112. <strong><a href=\"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-content\/uploads\/sites\/11\/2016\/09\/2013mbs.pdf\">pdf<\/a><\/strong><\/li>\n<li>Q. Yang, X. Mao.<br \/>\n<cite>Extinction and recurrence of multi-group SEIR epidemic models with stochastic perturbations<\/cite>.<br \/>\nNonlinear Analysis: Real World Applications, 14 (2013) 1434-1456.<\/li>\n<li>Z. Wang, X. Fan, Q. Han.<br \/>\n<cite>Global stability of deterministic and stochastic multigroup SEIQR models in computer network<\/cite>.<br \/>\nApplied Mathematical Modelling, 37 (2013) 8673-8686.<\/li>\n<li>W. Li, H. Song, Y. Qu, K. Wang.<br \/>\n<cite>Global exponential stability for stochastic coupled systems on networks with Markovian switching<\/cite>.<br \/>\nSystems &amp; Control Letters, 62 (2013) 468-474.<\/li>\n<li>X. Yuan, Y. Xue, M. Liu.<br \/>\n<cite>Analysis of an epidemic model with awareness programs by media on complex networks<\/cite>.<br \/>\nChaos, Solitons &amp; Fractals, 48 (2013) 1-11.<\/li>\n<li>Y. Muroya, Y. Enatsu, T. Kuniya.<br \/>\n<cite>Global stability for a multi-group SIRS epidemic model with varying population sizes<\/cite>.<br \/>\nNonlinear Analysis: Real World Applications, 14 (2013) 1693-1704.<\/li>\n<li>T. Kuniya.<br \/>\n<cite>Global stability of a multi-group SVIR epidemic model<\/cite>.<br \/>\nNonlinear Analysis: Real World Applications, 14 (2013) 1135-1143.<\/li>\n<li>C. Zhang, W. Li, K. Wang.<br \/>\n<cite>Boundedness for network of stochastic coupled van der Pol oscillators with time-varying delayed coupling<\/cite>.<br \/>\nApplied Mathematical Modelling, 37 (2013) 5394-5402.<\/li>\n<li>C. Zhang, W. Li, H. Su, K. Wang.<br \/>\n<cite>A graph-theoretic approach to boundedness of stochastic Cohen\u00d0Grossberg neural networks with Markovian switching<\/cite>.<br \/>\nApplied Mathematics and Computation, 219 (2013) 9165-9173.<\/li>\n<li>Y. Muroya, Y. Enatsu, T. Kuniya.<br \/>\n<cite>Global stability of extended multi-group sir epidemic models with patches through migration and cross patch infection<\/cite>.<br \/>\nActa Mathematica Scientia, 33 (2013) 341-361.<\/li>\n<li>M.-T. Li, G.-Q. Sun, J. Zhang, Z. Jin.<br \/>\n<cite>Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission<\/cite>.<br \/>\nDiscrete Dynamics in Nature and Society, (2013) 703826.<\/li>\n<li>Y.-W. Gong, Y.-R. Song, G.-P. Jiang.<br \/>\n<cite>Global dynamics of a novel multi-group model for computer worms<\/cite>.<br \/>\nChinese Physics B, 22 (2013) 040204.<\/li>\n<li>H. Su, Y. Qu, S. Gao, H. Song, K. Wang.<br \/>\n<cite>A model of feedback control system on network and its stability analysis<\/cite>.<br \/>\nCommunications in Nonlinear Science and Numerical Simulation, 18 (2013) 1822-1831.<\/li>\n<li>Y. Lin, D. Jiang.<br \/>\n<cite>Dynamics of a multigroup SIR epidemic model with nonlinear incidence and stochastic perturbation<\/cite>.<br \/>\nAbstract and Applied Analysis, (2013) 917389.<\/li>\n<li>L. Zhang, J. Pang, J. Wang.<br \/>\n<cite>Stability analysis of a multigroup epidemic model with general exposed distribution and nonlinear incidence rates<\/cite>.<br \/>\nAbstract and Applied Analysis, (2013) 354287.<\/li>\n<li>P. Du, M.Y. Li.<br \/>\n<cite>Impact of network connectivity on the synchronization and global dynamics of coupled systems of differential equations<\/cite>.<br \/>\nPhysica D: Nonlinear Phenomena, 286 (2014) 32-42.<\/li>\n<li>J. Wang, J. Wang, M. Liu, Y. Li.<br \/>\n<cite>Global stability analysis of an SIR epidemic model with demographics and time delay on networks<\/cite>.<br \/>\nPhysica A: Statistical Mechanics and its Applications, 410 (2014) 268-275.<\/li>\n<li>T. Kuniya, Y. Muroya.<br \/>\n<cite>Global stability of a multi-group SIS epidemic model for population migration<\/cite>.<br \/>\nDiscrete and Continuous Dynamical Systems Series B, 19 (2014) 1105-1118.<\/li>\n<li>C. Zhang, W. Li, K. Wang.<br \/>\n<cite>A graph-theoretic approach to stability of neutral stochastic coupled oscillators network with time?varying delayed coupling<\/cite>.<br \/>\nMathematical Methods in the Applied Sciences, 37 (2014) 1179-1190.<\/li>\n<li>J. Wang, J. Pang, X. Liu.<br \/>\n<cite>Modelling diseases with relapse and nonlinear incidence of infection: a multi-group epidemic model<\/cite>.<br \/>\nJournal of Biological Dynamics, 8 (2014) 99-116.<\/li>\n<li>T. Kuniya, Y. Muroya, Y. Enatsu.<br \/>\n<cite>Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures<\/cite>.<br \/>\nMathematical Biosciences and Engineering, 11 (2014) 1375-1393.<\/li>\n<li>Y. Wang, J. Cao.<br \/>\n<cite>Global dynamics of a network epidemic model for waterborne diseases spread<\/cite>.<br \/>\nApplied Mathematics and Computation, 237 (2014) 474-488.<\/li>\n<li>W. Li, X. Qi, M. Pan, K. Wang.<br \/>\n<cite>Razumikhin-type theorems on exponential stability of stochastic functional differential equations on networks<\/cite>.<br \/>\nNeurocomputing, 131 (2014) 278-285.<\/li>\n<li>C. Zhang, W. Li, H. Su, K. Wang.<br \/>\n<cite>Asymptotic boundedness for stochastic coupled systems on networks with Markovian switching<\/cite>.<br \/>\nNeurocomputing, 136 (2014) 180-189.<\/li>\n<li>Z.-G. Wang, R.-M. Gao, X.-M. Fan, Q.-X. Han.<br \/>\n<cite>Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate<\/cite>.<br \/>\nChinese Physics B, 23 (2014) 090201.<\/li>\n<li>W. Li, H. Yang, J. Feng, K. Wang.<br \/>\n<cite>Global exponential stability for coupled systems of neutral delay differential equations<\/cite>.<br \/>\nElectronic Journal of Qualitative Theory of Differential Equations, 36 (2014) 1-15.<\/li>\n<li>X. Yuan, Y. Xue, M. Liu.<br \/>\n<cite>Global stability of an SIR model with two susceptible groups on complex networks<\/cite>.<br \/>\nChaos, Solitons &amp; Fractals, 59 (2014) 42-50.<\/li>\n<li>Y. Wang, J. Cao.<br \/>\n<cite>Global dynamics of multi-group SEI animal disease models with indirect transmission<\/cite>.<br \/>\nChaos, Solitons &amp; Fractals, 69 (2014) 81-89.<\/li>\n<li>Y. Muroya, T. Kuniya.<br \/>\n<cite>Further stability analysis for a multi-group SIRS epidemic model with varying total population size<\/cite>.<br \/>\nApplied Mathematics Letters, 38 (2014) 73-78.<\/li>\n<li>M.-T. Li, G.-Q. Sun, Y.-F. Wu, J. Zhang, Z. Jin.<br \/>\n<cite>Transmission dynamics of a multi-group brucellosis model with mixed cross infection in public farm<\/cite>.<br \/>\nApplied Mathematics and Computation, 237 (2014) 582-594.<\/li>\n<li>Y. Xue, X. Yuan, M. Liu.<br \/>\n<cite>Global stability of a multi-group SEI model<\/cite>.<br \/>\nApplied Mathematics and Computation, 226 (2014) 51-60.<\/li>\n<li>G. Huang, J. Wang, J. Zu.<br \/>\n<cite>Global dynamics of multi-group dengue disease model with latency distributions<\/cite>.<br \/>\nMathematical Methods in the Applied Sciences, (2014) DOI: 10.1002\/mma.3252.<\/li>\n<li>W. Li, H. Yang, L. Wen, K. Wang.<br \/>\n<cite>Global exponential stability for coupled retarded systems on networks: A graph-theoretic approach<\/cite>.<br \/>\nCommunications in Nonlinear Science and Numerical Simulation, 19 (2014) 1651-1660.<\/li>\n<li>Y. Wang, J. Cao.<br \/>\n<cite>Global stability of a multiple infected compartments model for waterborne diseases<\/cite>.<br \/>\nCommunications in Nonlinear Science and Numerical Simulation, 19 (2014) 3753-3765.<\/li>\n<li>Z. Wang, X. Fan, F. Jiang, Q. Li.<br \/>\n<cite>Dynamics of deterministic and stochastic multi-group MSIRS epidemic models with varying total population size<\/cite>.<br \/>\nAdvances in Difference Equations, (2014): 270.<\/li>\n<li>H. Li, Y. Jiang, L. Zhang, Z. Teng.<br \/>\n<cite>Global Stability for a Three-Species Food Chain Model in a Patchy Environment<\/cite>.<br \/>\nJournal of Applied Mathematics, (2014) 314729.<\/li>\n<li>X. Zhong, F. Deng.<br \/>\n<cite>Dynamics of a Stochastic Multigroup SEIR Epidemic Model<\/cite>.<br \/>\nJournal of Applied Mathematics, (2014) 258915.<\/li>\n<li>J.C. Kamgang, V.C. Kamla, S.Y. Tchoumi.<br \/>\n<cite>Modeling the Dynamics of Malaria Transmission with Bed Net Protection Perspective<\/cite>.<br \/>\nApplied Mathematics, 5 (2014) 3156.<\/li>\n<li>X. Fan.<br \/>\n<cite>Global stability of multigroup SIRS epidemic model with varying population sizes and stochastic perturbation around equilibrium<\/cite>.<br \/>\nAbstract and Applied Analysis, (2014) 154725.<\/li>\n<li>Y. Gao, S. Liu.<br \/>\n<cite>Global stability for a predator-prey model with dispersal among patches<\/cite>.<br \/>\nAbstract and Applied Analysis, (2014) 176493.<\/li>\n<li>N. Wang, J. Pang, J. Wang.<br \/>\n<cite>Stability Analysis of a Multigroup SEIR Epidemic Model with General Latency Distributions<\/cite>.<br \/>\nAbstract and Applied Analysis, (2014) 740256.<\/li>\n<li>Z. Shuai, P. van den Driessche.<br \/>\n<cite>Modelling and control of cholera on networks with a common water source<\/cite>.<br \/>\nJournal of Biological Dynamics, in press.<\/li>\n<li>J. Ren, Y. Xu, J. Liu.<br \/>\n<cite>Investigation of dynamics of a virus-antivirus model in complex network<\/cite>.<br \/>\nPhysica A: Statistical Mechanics and its Applications, 421 (2015) 533-540.<\/li>\n<li>C. Zhang, W. Li, K. Wang.<br \/>\n<cite>Graph-theoretic approach to stability of multi-group models with dispersal<\/cite>.<br \/>\nDiscrete and Continuous Dynamical Systems Series B, 20 (2015) 259-280.<\/li>\n<li>X. Feng, Z. Teng, F. Zhang.<br \/>\n<cite>Global dynamics of a general class of multi-group epidemic models with latency and relapse<\/cite>.<br \/>\nMathematical Biosciences and Engineering, 12 (2015) 99-115.<\/li>\n<li>Y. Muroya, T. Kuniya, J. Wang.<br \/>\n<cite>Stability analysis of a delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure<\/cite>.<br \/>\nJournal of Mathematical Analysis and Applications, 425 (2015) 415-439.<\/li>\n<li>X. Zhang, W. Li, K. Wang.<br \/>\n<cite>The existence of periodic solutions for coupled systems on networks with time delays<\/cite>.<br \/>\nNeurocomputing, 152 (2015) 287-293.<\/li>\n<li>W. Li, S. Wang, H. Su, K. Wang.<br \/>\n<cite>Global exponential stability for stochastic networks of coupled oscillators with variable delay<\/cite>.<br \/>\nCommunications in Nonlinear Science and Numerical Simulation, 22 (2015) 877-888.<\/li>\n<li>C. Zhang, W. Li, K. Wang.<br \/>\n<cite>Graph-theoretic method on exponential synchronization of stochastic coupled networks with Markovian switching<\/cite>.<br \/>\nNonlinear Analysis: Hybrid Systems, 15 (2015) 37-51.<\/li>\n<li>J. Cai, Y. Wang, A. Alofi, A. Al-Mazrooei, A. Elaiw.<br \/>\n<cite>Global stability of an epidemic model with carrier state in heterogeneous networks<\/cite>.<br \/>\nIMA Journal of Applied Mathematics, in press.<\/li>\n<li>H. Su, Z. He, Y. Zhao, X. Ding.<br \/>\n<cite>A graph-theoretic approach to exponential stability of BAM neural networks with delays and reaction-diffusion<\/cite>.<br \/>\nApplicable Analysis, in press.<\/li>\n<li>W. Li, X. Zhang, C. Zhang.<br \/>\n<cite>A new method for exponential stability of coupled reaction-diffusion systems with mixed delays: Combining Razumikhin method with graph theory<\/cite>.<br \/>\nJournal of the Franklin Institute, in press.<\/li>\n<li>Hong-Li Li, Yao-Lin Jiang, Zuo-Lei Wang, Cheng Hu.<br \/>\n<cite>Global stability problem for feedback control systems of impulsive fractional differential equations on networks<\/cite>.<br \/>\nNeurocomputing, in press.<\/li>\n<li>A. Iggidr, G. Sallet, M.O. Souza.<br \/>\n<cite>On the dynamics of a class of multi-group models for vector-borne diseases<\/cite>.<br \/>\nPreprint.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>A Graph-Theoretic Approach to the Construction of Lyapunov Functions for Large-Scale Differential Equation Systems \u00a0\u00a0* Please contact me via email (shuai@ucf.edu) to add\/remove a paper from this list Theoretical Development on the Graph-Theoretic Approach H. Guo, M.Y. Li, Z. Shuai. Global stability of the endemic equilibrium of multigroup SIR epidemic models. Canadian Applied Mathematics Quarterly, [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-18","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/pages\/18","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/comments?post=18"}],"version-history":[{"count":0,"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/pages\/18\/revisions"}],"wp:attachment":[{"href":"https:\/\/sciences.ucf.edu\/math\/zshuai\/wp-json\/wp\/v2\/media?parent=18"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}