Stability and controllability of cycled dynamical systems
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Yuanlin Ding
Abstract
In this paper, we consider a new type of dynamical systems called cycled dynamical systems (CDSs) based on the cell growth and division process. Firstly, the existence and uniqueness of cycled solutions of CDSs are studied. Secondly, we present the solutions of the CDSs through an appropriate cycled Cauchy matrix. Moreover, the stability of the linear homogeneous problems, linear perturbation problems and nonlinear problems is analyzed. Next, we investigate the controllability of linear and nonlinear CDSs. Finally, theoretical results are illustrated by providing examples.
Funding statement: This work is partially supported by the National Natural Science Foundation of China (12161015), the Slovak Research and Development Agency under the contract No. APVV-23-0039, and the Slovak Grant Agency VEGA No. 1/0084/23 and No. 2/0062/24.
(Communicated by Irena Jadlovská)
References
[1] Barančok, P.: Mathematical Models in Yeast Biology, Comenius University, Bratislava, 2020.Search in Google Scholar
[2] Elaydi, S.: An Introduction to Difference Equations, Springer-Verlag, New York, 2005.Search in Google Scholar
[3] Fečkan, M.—Wang, J.—Zhou, Y.: Controllability of fractional functional evolution equations of Sobolev type via characteristic solution operators, J. Optim. Theory Appl. 156 (2013), 79–95.Search in Google Scholar
[4] Ferrezuelo, F.—Colomina, N.—Palmisano, A.—Garí, E.—Gallego, C.—Csikász-Nagy, A.—Aldea, M.: The critical size is set at a single-cell level by growth rate to attain homeostasis and adaptation, Nat. Commun. 3 (2012), Art. ID 1012.Search in Google Scholar
[5] Hutchings, N. J.—Gordon, I. J.: A dynamic model of herbivore-plant interactions on grasslands, Ecological Modelling 136 (2001), 209–222.Search in Google Scholar
[6] Irwin, M. C.: Smooth Dynamical Systems, Academic Press, London, 1980.Search in Google Scholar
[7] Ji, S.—Li, G.—Wang, M.: Controllability of impulsive differential systems with nonlocal conditions, Appl. Math. Comput. 217 (2011), 6981–6989.Search in Google Scholar
[8] Kalman, R. E.: Contributions to the theory of optimal control, Bol. Soc. Mat. Mex. 5 (1960), 102–119.Search in Google Scholar
[9] Kumar, A.—Muslim, M.—Sakthivel, R.: Controllability of the second-order nonlinear differential equations with non-instantaneous impulses, J. Dyn. Control Syst. 24 (2018), 325–342.Search in Google Scholar
[10] Liu, S.—Wang, J.—Zhou, Y.: Optimal control of non-instantaneous impulsive differential equations, J. Franklin Inst. 354 (2017), 7668–7698.Search in Google Scholar
[11] Lyapunov, A. M.: The general problem of the stability of motion, Int. J. Control 55 (1992), 531–534.Search in Google Scholar
[12] Malone, M. A.—Halloway, A. H.—Brown, J. S.: The ecology of fear and inverted biomass pyramids, Oikos 129 (2020), 787–798.Search in Google Scholar
[13] Medveď, M.—Pospíšil, M.: Sufficient conditions for the asymptotic stability of nonlinear multidelay differential equations with linear parts defined by pairwise permutable matrices, Nonlinear Anal. Theory Methods Appl. 75 (2012), 3348–3363.Search in Google Scholar
[14] Rafelski, S. M.—Viana, M. P.—Zhang, Y.—Chan, Y. H.—Thorn, K. S.—Yam, P.—Fung, J. C.— Li, H.—Costa, L. F.—Marshall, W. F.: Mitochondrial network size scaling in budding yeast, Science 338 (2012), 822–824.Search in Google Scholar
[15] Roberts, M. G.—Hickson, R. I.—Mccaw, J. M.: How immune dynamics shape multi-season epidemics: a continuous-discrete model in one dimensional antigenic space, J. Math. Biol. 88 (2024), Art. No. 48.Search in Google Scholar
[16] Samoilenko, A. M.—Perestyuk, N. A.—Chapovsky, Y.: Impulsive Differential Equations, World Scientific, Singapore, 1995.Search in Google Scholar
[17] Sharma, S.—Samanta, G. P.: A ratio-dependent predator-prey model with Allee effect and disease in prey, J. Appl. Math. Comput. 47 (2015), 345–364.Search in Google Scholar
[18] Wang, Y.—Li, Y.—Ren, X.—Liu, X.: A periodic dengue model with diapause effect and control measures, Appl. Math. Model. 108 (2022), 469–488.Search in Google Scholar
[19] Wang, J.—Fečkan, M.—Tian, Y.: Stability analysis for a general class of noninstantaneous impulsive differential equations, Mediterr. J. Math. 14 (2017), 1–21.Search in Google Scholar
[20] Wang, J.—Fečkan, M.—Zhou, Y.: Controllability of Sobolev type fractional evolution systems, Dyn. Partial Differ. Equ. 11 (2014), 71–87.Search in Google Scholar
[21] You, Z.—Wang, J.: Stability of impulsive delay differential equations, J. Appl. Math. Comput. 56 (2018), 253–268.Search in Google Scholar
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Articles in the same Issue
- Copies of monomorphic structures
- Endomorphism kernel property for extraspecial and special groups
- Sums of Tribonacci numbers close to powers of 2
- Multiplicative functions k-additive on hexagonal numbers
- Monogenic even cyclic sextic polynomials
- Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function
- Degree of independence in non-archimedean fields
- Remarks on some one-ended groups
- Some new characterizations of weights for hardy-type inequalities with kernels on time scales
- Inequalities for Riemann–Liouville fractional integrals in co-ordinated convex functions: A Newton-type approach
- Radius estimates for functions in the class 𝒰r(λ)
- Sharp bounds on the logarithmic coefficients of inverse functions for certain classes of univalent functions
- More q-congruences from Singh’s quadratic transformation
- Stability and controllability of cycled dynamical systems
- Existence, uniqueness, and multiplicity of radially symmetric k-admissible solutions for k-hessian equations
- Strong solution of a Navier-Stokes-Cahn-Hilliard system for incompressible two-phase flows with surfactant
- Coincidence points via tri-simulation functions with an application in integral equations
- On Fong-Tsui conjecture and binormality of operators
- Riemannian maps of CR-submanifolds of Kaehler manifolds
- On structural numbers of topological spaces
- The κ-Fréchet-Urysohn property for Cp(X) is equivalent to baireness of B1(X)
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