Periodic solutions for feedback control coupled systems on networks

References

• Strogatz S. Exploring complex networks. Nature. 2001;410(6825):268–276.
   PubMed Web of Science ®Google Scholar
• Boccaletti S, Latora V, Moreno Y, et al. Complex networks: structure and dynamics. Phys Rep. 2006;424(4):175–308.
   Web of Science ®Google Scholar
• Yang X, Cao J. Finite-time stochastic synchronization of complex networks. Appl Math Model. 2010;34(11):3631–3641.
   Web of Science ®Google Scholar
• Gao S, Wu B. On input-to-state stability for stochastic coupled control systems on networks. Appl Math Comput. 2015;262:90–101.
   Web of Science ®Google Scholar
• Tan X, Cao J. Intermittent control with double event-driven for leader-following synchronization in complex networks. Appl Math Model. 2018;64:372–385.
   Web of Science ®Google Scholar
• Gao S, Wang Q, Wu B. Existence and global exponential stability of periodic solutions for coupled control systems on networks with feedback and time delays. Commun Nonlinear Sci Numer Simul. 2018;63:72–87.
   Web of Science ®Google Scholar
• Dunbar W. Distributed receding horizon control of dynamically coupled nonlinear systems. IEEE Trans Autom Control. 2007;52(7):1249–1263.
   Web of Science ®Google Scholar
• Wu Y, Wang C, Li W. Generalized quantized intermittent control with adaptive strategy on finite-time synchronization of delayed coupled systems and applications. Nonlinear Dyn. 2019;95(2):1361–1377.
   Web of Science ®Google Scholar
• Wang P, Feng J, Su H. Stabilization of stochastic delayed networks with Markovian switching and hybrid nonlinear coupling via aperiodically intermittent control. Nonlinear Anal-Hybrid Syst. 2019;32:115–130.
   Web of Science ®Google Scholar
• Liu Y, Zhang D, Su H. Stationary distribution for stochastic coupled systems with regime switching and feedback control. Physica A. 2019;535:122221.
   Google Scholar
• Xu Y, Zhou H, Li W. Stabilisation of stochastic delayed systems with lévy noise on networks via periodically intermittent control. Int J Control. 2020;93(3):505–518.
   Web of Science ®Google Scholar
• Lefschetz S. Stability of nonlinear control systems. London: Academic Press; 1965.
   Google Scholar
• Slotine J, Li W. Applied nonlinear control. NJ Englewood Cliffs: Prentice Hall; 1991.
   Google Scholar
• Vidyasagar M. Nonlinear systems analysis. NJ Englewood Cliffs: Prentice-Hall; 1993.
   Google Scholar
• Zhang X, Jiang D, Alsaedi A, et al. Periodic solutions and stationary distribution of mutualism models in random environments. Physica A. 2016;460:270–282.
   Web of Science ®Google Scholar
• Kamachkin A, Potapov D, Yevstafyeva V. Existence of periodic solutions to automatic control system with relay nonlinearity and sinusoidal external influence. Int J Robust Nonlinear Control. 2017;27(2):204–211.
   Web of Science ®Google Scholar
• Yan Y, Sugie J. Existence regions of positive periodic solutions for a discrete hematopoiesis model with unimodal production functions. Appl Math Model. 2019;68:152–168.
   Web of Science ®Google Scholar
• Song K, Zhang T, Ma W. Nontrivial periodic solution of a stochastic non-autonomous model with biodegradation of microcystins. Appl Math Lett. 2019;94:87–93.
   Web of Science ®Google Scholar
• Yao Q, Wang L, Wang Y. Periodic solutions to impulsive stochastic reaction-diffusion neural networks with delays. Commun Nonlinear Sci Numer Simul. 2019;78:104865.
   Google Scholar
• Cao J. On exponential stability and periodic solutions of CNNs with delays. Phys Lett A. 2000;267:312–318.
   Web of Science ®Google Scholar
• Fan M, Wang K. Global existence of positive periodic solutions of periodic predator-prey system with infinite delays. J Math Anal Appl. 2001;262:1–11.
   Web of Science ®Google Scholar
• Fan M, Wang K. Periodicity in a delayed ratio-dependent predator-prey system. J Math Anal Appl. 2001;262:179–190.
   Web of Science ®Google Scholar
• Wei J, Li M. Global existence of periodic solutions in a tri-neuron network model with delays. Phys D- Nonlinear Phenom. 2004;198:106–119.
   Web of Science ®Google Scholar
• Dragan V, Aberkane S, Ivanov I. On computing the stabilizing solution of a class of discrete-time periodic Riccati equations. Int J Robust Nonlinear Control. 2015;25(7):1066–1093.
   Web of Science ®Google Scholar
• Li M, Shuai Z. Global-stability problem for coupled systems of differential equations on networks. J Differ Equ. 2010;248(1):1–20.
   Web of Science ®Google Scholar
• Guo H, Li M, Shuai Z. Global dynamics of a general class of multistage models for infectious diseases. SIAM J Appl Math. 2012;72:261–279.
   Web of Science ®Google Scholar
• Guo Y, Zhao W, Ding X. Input-to-state stability for stochastic multi-group models with multi-dispersal and time-varying delay. Appl Math Comput. 2018;290:507–520.
   Google Scholar
• Guo B, Xiao Y, Zhang C. Synchronization analysis of stochastic coupled systems with time delay on networks by periodically intermittent control and graph-theoretic method. Nonlinear Anal-Hybrid Syst. 2018;30:118–133.
   Web of Science ®Google Scholar
• Wang M, Li W. Stability of random impulsive coupled systems on networks with Markovian switching. Stoch Anal Appl. 2019;37(6):1107–1132.
   Web of Science ®Google Scholar
• Liu Y, Yu P, Chu D, et al. Stationary distribution of stochastic multi-group models with dispersal and telegraph noise. Nonlinear Anal-Hybrid Syst. 2019;33:93–103.
   Web of Science ®Google Scholar
• Zhou H, Li W. Synchronisation of stochastic-coupled intermittent control systems with delays and Levy noise on networks without strong connectedness. IET Contr Theory Appl. 2019;13(1):36–49.
   Web of Science ®Google Scholar
• Guo Y, Liu Y, Xu Y. Synchronized stationary distribution of stochastic coupled systems based on graph theory. Math Meth Appl Sci. 2019;42(13):4444–4455.
   Web of Science ®Google Scholar
• Zhang C, Han BS. Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory. Physica A. 2020;538:122827.
   Web of Science ®Google Scholar
• Li S, Lv C, Ding X. Synchronization of stochastic hybrid coupled systems with multi-weights and mixed delays via aperiodically adaptive intermittent control. Nonlinear Anal-Hybrid Syst. 2020;35:100819.
   Web of Science ®Google Scholar
• Xu Y, Li W. Finite-time synchronization of fractional-order complex-valued coupled systems. Physica A. 2020;549:123903.
   Google Scholar
• West DB. Introduction to graph theory. London: Prentice Hall; 2001.
   Google Scholar
• Trudeau R. Introduction to graph theory. New York: Courier Dover Publications; 2013.
   Google Scholar
• Gaines R, Mawhin J. Coincidence degree and nonlinear differential equations. Berlin: Springer; 1977.
   Google Scholar
• Fan M, Wang K, Jiang D. Existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with several deviating arguments. Math Biosci. 1999;160:47–61.
   PubMed Web of Science ®Google Scholar
• Fan M, Wang K. Global periodic solutions of a generalized n-species Gilpin-Ayala competition model. Comput Math Appl. 2000;40:1141–1151.
   Web of Science ®Google Scholar
• Zhang X, Li W, Wang K. The existence of periodic solutions for coupled systems on networks with time delays. Neurocomputing. 2015;152:287–293.
   Web of Science ®Google Scholar
• Fiedler B, Belhaq M, Houssni M. Basins of attraction in strongly damped coupled mechanical oscillators: A global example. Z Angew Math Phys. 1999;50:282–300.
   Web of Science ®Google Scholar
• Du P, Li M. Impact of network connectivity on the synchronization and global dynamics of coupled systems of differential equations. Phys D- Nonlinear Phenom. 2014;286:32–42.
   Web of Science ®Google Scholar
• Wang P, Wang G, Su H. The existence and exponential stability of periodic solution for coupled systems on networks without strong connectedness. Neurocomputing. 2018;313:206–219.
   Web of Science ®Google Scholar