DYNAMIC BEHAVIOR OF THE SOLUTIONS FOR A FINANCIAL SYSTEM WITH DELAYS

CHUNHUA FENG *

Department of Mathematics and Computer Science, Alabama State University, Montgomery, USA.

*Author to whom correspondence should be addressed.


Abstract

Several four-dimensional financial systems with or without time delays have been discussed in the literature. In this paper, the dynamics of a general four-dimensional financial model with four delays is investigated. The dynamic behavior of the solutions is provided by using of the mathematical analysis method. Two sufficient conditions to guarantee the existence of the permanent oscillations for the model are obtained. It is shown that the permanent oscillations occur if there exists a unique unstable equilibrium and all solutions are bounded of the financial system. Numerical simulation is provided to demonstrate the proposed results.

Keywords: Financial system, delay, instability, oscillation


How to Cite

FENG, C. (2022). DYNAMIC BEHAVIOR OF THE SOLUTIONS FOR A FINANCIAL SYSTEM WITH DELAYS. Asian Journal of Mathematics and Computer Research, 29(4), 46–54. https://doi.org/10.56557/ajomcor/2022/v29i48052

Downloads

Download data is not yet available.

References

Pati NC, Ghosh B. Delayed carrying capacity induced subcritical and supercritical Hopf bifurcations in a predator-prey system. Math. Comput. Simul. 2022;195:171-196.

Zhang Y, Koura YH, Su Y. Dynamics of a delayed predator-prey model with application to network users' data forwarding. Nature: Scientic Report; 2019. Article No. 12535 (2019).

Jiao X, Li X, Yang Y. Dynamics and bifurcations of a Filippov Leslie-Gower predator-prey model with group defense and time delay. Chaos, Solit. Fract. 2022;162:112436.

Gupta A, Dubey B. Bifurcations and chaos in a delayed eco-epidwmic model induced by prey conguration. Chaos, Solit. Fract. 2022;165:112785.

Haque M, Sarwardi S, Preston S, Venturino E. Eect of delay in a Lotka-Volterra type predator- prey model with a transmissible disease in the predator species. Math. Biosci. 2011;234 :47-54.

Wang C, Li N, Zhou Y, Pu X, Li R. On a multi-delay Lotka-Volterra predator-prey model with feedback control and prey diusion. Acta Math. Scientia. 2019;39:429-448. Feng; AJOMCOR, 29(4): 46-54, 2022

Darabsah I, Chen L, Nicola W, Campbell S. The impact of small time delays on the onset of oscillations and synchrony in brain networks. Front. Syst. Neurosci. 2021;15 DOI: https://doi.org/10.3389/fnsys2021.88517

Zhang J, Huang C. Dynamics analysis on a class of delayed neural networks involving inertial terms. Advan. Di. Eqs; 2020. Article No. 120 (2020).

Berezansky L, Braverman E. On the global attractivity of non-autonomous neural networks with a distributed delay. Nonlinearity. 2021;34. DOI: https://doi 10.1088/1361-6544/abbc61

Munoz JJ, Dingle M, Wenzel M. Mechanical oscillations in biological tissues as a result of delayed rest-length changes. Phys. Rev. E. 2018;98:052409.

Shen S, Song A, Li H, Li T. Casecade predictor for a class of mechanical systems under large uncertain measurement delays. Mech. Syst. Sign. Proce. 2022;167:108536.

Segura RV. Delayed controllers for time-delay systems. Commun. Nonlinear Sci. Numer. Simulat. 2022;167:108536.

Ma JH, Chen YS. Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear nance system (I). Appl. Math. Mech. 2001;22:1240-1251.

Ma JH, Chen YS. Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear nance system (II). Appl. Math. Mech. 2001;22:1375-1382.

Ma JH, Ren B, Chen YS. Impulsive control of chaotic attractors in nonlinear chaotic systems. Appl. Math. Mech. 2004;25:889-894.

Ding J, Yang W, Yao H. A new modied hyperchaotic nance system and its control. Int. J. Nonlinear Science. 2009;8:59-66.

Chen WC. Dynamics and control of a nancial system with time-delayed feedbacks. Chaos, Solit. Fract. 2008;37:1198-1207.

Gao Q, Ma J. Chaos and Hopf bifurcation of a nance system. Nonlinear Dynamics. 2009;58 :209-216.

Wang Y, Zhai YH, Wang J, Chaos and Hopf bifurcation of a nance system with distributed time delay. Int. J. Appl. Math. Mech. 2010;6:1-13.

Son WS, Park YJ. Delayed feedback on the dynamical model of a nancial system. Chaos, Solit. Fract. 2011;44:208-217.

Zhang R. Bifurcation analysis for a kind of nonlinear nance system with delayed feedback and its application to control of chaos. J. Appl. Math; 2012. Article ID 316390. DOI: 10.1155/2012/316390

Kai G, Zhang W. Chaotic dynamics analysis for a class of delay nonlinear nance systems. In: MATEC Web of Conferences. 2016;45:03005. EDP Sciences

Ding Y, Jiang W, Wang H. Hopf-pitchfork bifurcation and periodic phenomena in nonlinear nancial system with delay. Chaos, Solit. Fract. 2012;45:1048-1057.

Wu W, Chen Z. Hopf bifurcation and intermittent transition to hyperchaos in a novel strong four-dimensional hyperchaotic system. Nonlinear Dynamics. 2010;60(2010):615-630.

Yu H, Cai G, Li Y. Dynamic analysis and control of a new hyperchaotic nance system. Nonlinear Dynamics. 2012;67:2171-2182.

Calis Y, Demirci A, Ozemir C. Hopf bifurcation of a nancial dynamical system with delay. Math. Comput. Simul. 2022;201:343-361. Feng; AJOMCOR, 29(4): 46-54, 2022

Shi J, He K, Fang H. Hopf bifurcation and control of a fractional-order delay nancial system. Math. Comput. Simul. 2022;194:348-364.

Ma J, Chen Y, Liu L. Hopf bifurcation and chaos of nancial system on condition of specic combination of parameters. J. Syst. Sci. Complexity. 2008;21:250-259.

Chafee N. A bifurcation problem for a functional dierential equation of nitely retarded type. J. Math. Anal. Appl. 1971;35:312-348.

Feng C, Plamondon R. An oscillatory criterion for a time delayed neural ring network model. Neural Networks. 2012;29-30:70-79.