A Graph-Theoretic Approach to the Construction of Lyapunov Functions for Large-Scale Differential Equation Systems
* 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, 14 (2006) 259-284. pdf - H. Guo, M.Y. Li, Z. Shuai.
A graph-theoretic approach to the method of global Lyapunov functions.
Proceedings of the American Mathematical Society, 136 (2008) 2793-2802. pdf - M.Y. Li, Z. Shuai.
Global-stability problem for coupled systems of differential equations on networks.
Journal of Differential Equations, 248 (2010) 1-20. pdf - Z. Shuai, P. van den Drissche.
Global stability of infectious disease models using Lyapunov functions.
SIAM Journal on Applied Mathematics, 73 (2013) 1513-1532. pdf
Application of the Graph-Theoretic Approach
- Y. Xiao, X. Zou.
Global stability in a model for interactions between two strains of host and one strain of parasite.
Canadian Applied Mathematics Quarterly, 16 (2008) 211-218. - M.Y. Li, Z. Shuai.
Global stability of an epidemic model in a patchy environment.
Canadian Applied Mathematics Quarterly, 17 (2009) 175-187. pdf - M.Y. Li, Z. Shuai, C. Wang.
Global stability of multi-group epidemic models with distributed delays.
Journal of Mathematical Analysis and Applications, 361 (2010) 38-47. pdf - Z. Yuan, L. Wang.
Global stability of epidemiological models with group mixing and nonlinear incidence rates.
Nonlinear Analysis: Real World Applications, 11 (2010) 995-1004. - R. Sun.
Global stability of the endemic equilibrium of multigroup SIR models with nonlinear incidence.
Computers & Mathematics with Applications, 60 (2010) 2286-2291. - Z. Yuan, X. Zou.
Global threshold property in an epidemic model for disease with latency spreading in a heterogeneous host population.
Nonlinear Analysis: Real World Applications, 11 (2010) 3479-3490. - Z. Shuai, P. van den Driessche.
Global dynamics of cholera models with differential infectivity.
Mathematical Biosciences, 234 (2011) 118-126. pdf - C. Ji, D. Jiang, N. Shi.
Multigroup SIR epidemic model with stochastic perturbation.
Physica A: Statistical Mechanics and its Applications, 390 (2011) 1747-1762. - G. Rozhnova, A. Nunes, A.J. McKane.
Stochastic oscillations in models of epidemics on a network of cities.
Physical Review E, 84 (2011) 051919. - R. Sun, J. Shi.
Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates.
Applied Mathematics and Computation, 218 (2011) 280-286. - H. Chen, J. Sun.
Global stability of delay multigroup epidemic models with group mixing and nonlinear incidence rates.
Applied Mathematics and computation, 218 (2011) 4391-4400. - T. Kuniya.
Global stability analysis with a discretization approach for an age-structured multigroup SIR epidemic model.
Nonlinear Analysis: Real World Applications, 12 (2011) 2640-2655. - D. Ding, X. Ding.
Global stability of multi-group vaccination epidemic models with delays.
Nonlinear Analysis: Real World Applications, 12 (2011) 1991-1997. - Z. Shuai, P. van den Driessche.
Impact of heterogeneity on the dynamics of an SEIR epidemic model.
Mathematical Biosciences and Engineering, 9 (2012) 393-411. pdf - H. Guo, M.Y. Li, Z. Shuai.
Global dynamics of a general class of multi-stage models for infectious diseases.
SIAM Journal on Applied Mathematics, 72 (2012) 261-279. pdf - H. Guo, M.Y. Li.
Impacts of migration and immigration on disease transmission dynamics in heterogeneous populations.
Discrete and Continuous Dynamical Systems Series B, 17 (2012) 2413-2430. - C. Ji, D. Jiang, Q. Yang, N. Shi.
Dynamics of a multigroup SIR epidemic model with stochastic perturbation.
Automatica, 48 (2012) 121-131. - K. Li, Z. Ma, Z. Jia, M. Small, X. Fu.
Interplay between collective behavior and spreading dynamics on complex networks.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 22 (2012) 043113. - H. Su, W. Li, K. Wang.
Global stability analysis of discrete-time coupled systems on networks and its applications.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 22 (2012) 033135. - H. Shu, D. Fan, J. Wei.
Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission.
Nonlinear Analysis: Real World Applications, 13 (2012) 1581-1592. - T. Kajiwara, T. Sasaki, Y. Takeuchi.
Construction of Lyapunov functionals for delay differential equations in virology and epidemiology.
Nonlinear Analysis: Real World Applications, 13 (2012) 1802-1826. - W. Li, L. Pang, H. Su, K. Wang.
Global stability for discrete CohenÐGrossberg neural networks with finite and infinite delays.
Applied Mathematics Letters, 25 (2012) 2246-2251. - W. Li, H. Su, D. Wei, K. Wang.
Global stability of coupled nonlinear systems with Markovian switching.
Communications in Nonlinear Science and Numerical Simulation, 17 (2012) 2609-2616. - C. Yuan, D. Jiang, D. O’Regan, R.P. Agarwal.
Stochastically asymptotically stability of the multi-group SEIR and SIR models with random perturbation.
Communications in Nonlinear Science and Numerical Simulation, 17 (2012) 2501-2516. - J. Wang, J. Zu, X. Liu, G. Huang, J. Zhang.
Global dynamics of a multi-group epidemic model with general relapse distribution and nonlinear incidence rate.
Journal of Biological Systems, 20 (2012) 235-258. - J. Wang, Y. Takeuchi, S. Liu.
A multi-group SVEIR epidemic model with distributed delay and vaccination.
International Journal of Biomathematics, 5 (2012) No. 3. - D. Ding, X. Wang, X. Ding.
Global stability of multigroup dengue disease transmission model.
Journal of Applied Mathematics, 2012 (2012) 342472. - M.C. Eisenberg, Z. Shuai, J.H. Tien, P. van den Driessche.
A cholera model in a patchy environment with water and human movement.
Mathematical Biosciences, 246 (2013) 105-112. pdf - Q. Yang, X. Mao.
Extinction and recurrence of multi-group SEIR epidemic models with stochastic perturbations.
Nonlinear Analysis: Real World Applications, 14 (2013) 1434-1456. - Z. Wang, X. Fan, Q. Han.
Global stability of deterministic and stochastic multigroup SEIQR models in computer network.
Applied Mathematical Modelling, 37 (2013) 8673-8686. - W. Li, H. Song, Y. Qu, K. Wang.
Global exponential stability for stochastic coupled systems on networks with Markovian switching.
Systems & Control Letters, 62 (2013) 468-474. - X. Yuan, Y. Xue, M. Liu.
Analysis of an epidemic model with awareness programs by media on complex networks.
Chaos, Solitons & Fractals, 48 (2013) 1-11. - Y. Muroya, Y. Enatsu, T. Kuniya.
Global stability for a multi-group SIRS epidemic model with varying population sizes.
Nonlinear Analysis: Real World Applications, 14 (2013) 1693-1704. - T. Kuniya.
Global stability of a multi-group SVIR epidemic model.
Nonlinear Analysis: Real World Applications, 14 (2013) 1135-1143. - C. Zhang, W. Li, K. Wang.
Boundedness for network of stochastic coupled van der Pol oscillators with time-varying delayed coupling.
Applied Mathematical Modelling, 37 (2013) 5394-5402. - C. Zhang, W. Li, H. Su, K. Wang.
A graph-theoretic approach to boundedness of stochastic CohenÐGrossberg neural networks with Markovian switching.
Applied Mathematics and Computation, 219 (2013) 9165-9173. - Y. Muroya, Y. Enatsu, T. Kuniya.
Global stability of extended multi-group sir epidemic models with patches through migration and cross patch infection.
Acta Mathematica Scientia, 33 (2013) 341-361. - M.-T. Li, G.-Q. Sun, J. Zhang, Z. Jin.
Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission.
Discrete Dynamics in Nature and Society, (2013) 703826. - Y.-W. Gong, Y.-R. Song, G.-P. Jiang.
Global dynamics of a novel multi-group model for computer worms.
Chinese Physics B, 22 (2013) 040204. - H. Su, Y. Qu, S. Gao, H. Song, K. Wang.
A model of feedback control system on network and its stability analysis.
Communications in Nonlinear Science and Numerical Simulation, 18 (2013) 1822-1831. - Y. Lin, D. Jiang.
Dynamics of a multigroup SIR epidemic model with nonlinear incidence and stochastic perturbation.
Abstract and Applied Analysis, (2013) 917389. - L. Zhang, J. Pang, J. Wang.
Stability analysis of a multigroup epidemic model with general exposed distribution and nonlinear incidence rates.
Abstract and Applied Analysis, (2013) 354287. - P. Du, M.Y. Li.
Impact of network connectivity on the synchronization and global dynamics of coupled systems of differential equations.
Physica D: Nonlinear Phenomena, 286 (2014) 32-42. - J. Wang, J. Wang, M. Liu, Y. Li.
Global stability analysis of an SIR epidemic model with demographics and time delay on networks.
Physica A: Statistical Mechanics and its Applications, 410 (2014) 268-275. - T. Kuniya, Y. Muroya.
Global stability of a multi-group SIS epidemic model for population migration.
Discrete and Continuous Dynamical Systems Series B, 19 (2014) 1105-1118. - C. Zhang, W. Li, K. Wang.
A graph-theoretic approach to stability of neutral stochastic coupled oscillators network with time?varying delayed coupling.
Mathematical Methods in the Applied Sciences, 37 (2014) 1179-1190. - J. Wang, J. Pang, X. Liu.
Modelling diseases with relapse and nonlinear incidence of infection: a multi-group epidemic model.
Journal of Biological Dynamics, 8 (2014) 99-116. - T. Kuniya, Y. Muroya, Y. Enatsu.
Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures.
Mathematical Biosciences and Engineering, 11 (2014) 1375-1393. - Y. Wang, J. Cao.
Global dynamics of a network epidemic model for waterborne diseases spread.
Applied Mathematics and Computation, 237 (2014) 474-488. - W. Li, X. Qi, M. Pan, K. Wang.
Razumikhin-type theorems on exponential stability of stochastic functional differential equations on networks.
Neurocomputing, 131 (2014) 278-285. - C. Zhang, W. Li, H. Su, K. Wang.
Asymptotic boundedness for stochastic coupled systems on networks with Markovian switching.
Neurocomputing, 136 (2014) 180-189. - Z.-G. Wang, R.-M. Gao, X.-M. Fan, Q.-X. Han.
Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate.
Chinese Physics B, 23 (2014) 090201. - W. Li, H. Yang, J. Feng, K. Wang.
Global exponential stability for coupled systems of neutral delay differential equations.
Electronic Journal of Qualitative Theory of Differential Equations, 36 (2014) 1-15. - X. Yuan, Y. Xue, M. Liu.
Global stability of an SIR model with two susceptible groups on complex networks.
Chaos, Solitons & Fractals, 59 (2014) 42-50. - Y. Wang, J. Cao.
Global dynamics of multi-group SEI animal disease models with indirect transmission.
Chaos, Solitons & Fractals, 69 (2014) 81-89. - Y. Muroya, T. Kuniya.
Further stability analysis for a multi-group SIRS epidemic model with varying total population size.
Applied Mathematics Letters, 38 (2014) 73-78. - M.-T. Li, G.-Q. Sun, Y.-F. Wu, J. Zhang, Z. Jin.
Transmission dynamics of a multi-group brucellosis model with mixed cross infection in public farm.
Applied Mathematics and Computation, 237 (2014) 582-594. - Y. Xue, X. Yuan, M. Liu.
Global stability of a multi-group SEI model.
Applied Mathematics and Computation, 226 (2014) 51-60. - G. Huang, J. Wang, J. Zu.
Global dynamics of multi-group dengue disease model with latency distributions.
Mathematical Methods in the Applied Sciences, (2014) DOI: 10.1002/mma.3252. - W. Li, H. Yang, L. Wen, K. Wang.
Global exponential stability for coupled retarded systems on networks: A graph-theoretic approach.
Communications in Nonlinear Science and Numerical Simulation, 19 (2014) 1651-1660. - Y. Wang, J. Cao.
Global stability of a multiple infected compartments model for waterborne diseases.
Communications in Nonlinear Science and Numerical Simulation, 19 (2014) 3753-3765. - Z. Wang, X. Fan, F. Jiang, Q. Li.
Dynamics of deterministic and stochastic multi-group MSIRS epidemic models with varying total population size.
Advances in Difference Equations, (2014): 270. - H. Li, Y. Jiang, L. Zhang, Z. Teng.
Global Stability for a Three-Species Food Chain Model in a Patchy Environment.
Journal of Applied Mathematics, (2014) 314729. - X. Zhong, F. Deng.
Dynamics of a Stochastic Multigroup SEIR Epidemic Model.
Journal of Applied Mathematics, (2014) 258915. - J.C. Kamgang, V.C. Kamla, S.Y. Tchoumi.
Modeling the Dynamics of Malaria Transmission with Bed Net Protection Perspective.
Applied Mathematics, 5 (2014) 3156. - X. Fan.
Global stability of multigroup SIRS epidemic model with varying population sizes and stochastic perturbation around equilibrium.
Abstract and Applied Analysis, (2014) 154725. - Y. Gao, S. Liu.
Global stability for a predator-prey model with dispersal among patches.
Abstract and Applied Analysis, (2014) 176493. - N. Wang, J. Pang, J. Wang.
Stability Analysis of a Multigroup SEIR Epidemic Model with General Latency Distributions.
Abstract and Applied Analysis, (2014) 740256. - Z. Shuai, P. van den Driessche.
Modelling and control of cholera on networks with a common water source.
Journal of Biological Dynamics, in press. - J. Ren, Y. Xu, J. Liu.
Investigation of dynamics of a virus-antivirus model in complex network.
Physica A: Statistical Mechanics and its Applications, 421 (2015) 533-540. - C. Zhang, W. Li, K. Wang.
Graph-theoretic approach to stability of multi-group models with dispersal.
Discrete and Continuous Dynamical Systems Series B, 20 (2015) 259-280. - X. Feng, Z. Teng, F. Zhang.
Global dynamics of a general class of multi-group epidemic models with latency and relapse.
Mathematical Biosciences and Engineering, 12 (2015) 99-115. - Y. Muroya, T. Kuniya, J. Wang.
Stability analysis of a delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure.
Journal of Mathematical Analysis and Applications, 425 (2015) 415-439. - X. Zhang, W. Li, K. Wang.
The existence of periodic solutions for coupled systems on networks with time delays.
Neurocomputing, 152 (2015) 287-293. - W. Li, S. Wang, H. Su, K. Wang.
Global exponential stability for stochastic networks of coupled oscillators with variable delay.
Communications in Nonlinear Science and Numerical Simulation, 22 (2015) 877-888. - C. Zhang, W. Li, K. Wang.
Graph-theoretic method on exponential synchronization of stochastic coupled networks with Markovian switching.
Nonlinear Analysis: Hybrid Systems, 15 (2015) 37-51. - J. Cai, Y. Wang, A. Alofi, A. Al-Mazrooei, A. Elaiw.
Global stability of an epidemic model with carrier state in heterogeneous networks.
IMA Journal of Applied Mathematics, in press. - H. Su, Z. He, Y. Zhao, X. Ding.
A graph-theoretic approach to exponential stability of BAM neural networks with delays and reaction-diffusion.
Applicable Analysis, in press. - W. Li, X. Zhang, C. Zhang.
A new method for exponential stability of coupled reaction-diffusion systems with mixed delays: Combining Razumikhin method with graph theory.
Journal of the Franklin Institute, in press. - Hong-Li Li, Yao-Lin Jiang, Zuo-Lei Wang, Cheng Hu.
Global stability problem for feedback control systems of impulsive fractional differential equations on networks.
Neurocomputing, in press. - A. Iggidr, G. Sallet, M.O. Souza.
On the dynamics of a class of multi-group models for vector-borne diseases.
Preprint.