An Effective Algorithm for the Stability and Bifurcation in a DDE Model of Gene Expression
Source abstract
Abstract
The stability and Hopf bifurcation of gene expression models with a mechanism of delayed state feedback are considered. An effective algorithm for the calculations on the delay stable interval of the equilibrium point, the direction, and stability of the bifurcating periodic solution is also proposed. The τ-decomposition strategy is applied to tackle the issue of local stability, and the explicit formula for the delay stable interval is provided. In addition, the asymptotical behaviors of the bifurcation solutions are investigated by the center manifold theorem and normal form theory. The direction and stability of the Hopf bifurcation are determined naturally. In addition, a subtle bilinear form of the adjoint system is proposed to calculate the bifurcation parameters directly. Finally, the correctness and effectiveness of our results and algorithm are verified by typical numerical examples.
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Research context
OpenAlex topics: Gene Regulatory Network Analysis · stochastic dynamics and bifurcation · Mathematical and Theoretical Epidemiology and Ecology Models
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Collage of Engineering, Hebei Normal University, Shijiazhuang 050024, China
References (31)
Show source-provided references
1. Hopf bifurcation in a DDE model of gene expression10.1016/j.cnsns.2006.05.001 ↗
2. Hopf bifurcation analysis in a model of oscillatory gene expression with delay10.1017/S0308210507000091 ↗
3. Oscillatory behavior in enzymatic control processes10.1016/0065-2571(65)90067-1 ↗
4. Oscillation and Chaos in Physiological Control Systems10.1126/science.267326 ↗
5. Existence criteria of periodic oscillations in cyclic gene regulatory networks10.1016/j.automatica.2011.02.042 ↗
6. Design principles of biochemical oscillators10.1038/nrm2530 ↗
7. Hopf bifurcation analysis for a model of single genetic negative feedback autoregulatory system with delay10.1016/j.neucom.2012.07.021 ↗
8. Dynamic Analysis of the Time-Delayed Genetic Regulatory Network Between Two Auto-Regulated and Mutually Inhibitory Genes10.1007/s11538-020-00722-1 ↗
9. Pattern formations of a delayed diffusive predator-prey model with predator harvesting and prey social behavior10.1002/mma.7340 ↗
10. Global analysis of an infection age model with a class of nonlinear incidence rates10.1016/j.jmaa.2015.09.066 ↗
11. Hopf bifurcation formula for first order differential-delay equations10.1016/j.cnsns.2005.08.005 ↗
12. Stability and Hopf bifurcation analysis for the diffusive delay logistic population model with spatially heterogeneous environment10.1016/j.amc.2021.126362 ↗
13. Mathematical analysis of a biochemical oscillator with delay10.1016/j.cam.2015.04.029 ↗
14. Multiple Scales without Center Manifold Reductions for Delay Differential Equations near Hopf Bifurcations10.1023/A:1021220117746 ↗
15. Stability and Bifurcation Analysis of a Diffusive miR-9/Hes1 Network With Time Delay10.1109/TCBB.2021.3050006 ↗
16. Hopf bifurcation analysis for models on genetic negative feedback loops10.1016/j.jmaa.2022.126537 ↗
17. Stability and bifurcations in fractional-order gene regulatory networks10.1016/j.amc.2022.126916 ↗
18. On zeroes of some transcendental equation
19. Cai, T.Y., Jin, H.L., Yu, H., and Xie, X.P. (2021). On Stability Switches and Bifurcation of the Modified Autonomous Van der Polduffing Equations via Delayed State Feedback Control. Symmetry, 13.10.3390/sym13122336 ↗
20. Spatiotemporal patterns induced by cross-diffusion in predator prey model with prey herd shape effect10.1142/S1793524520500308 ↗
21. Rand, R.H. (2023, February 01). Available online: http://www.tam.cornell.edu/randdocs/nlvibe54.pdf.
22. Bifurcation analysis of a diffusive predator–prey model with prey social behavior and predator harvesting10.1002/mma.7807 ↗
23. Subcritical Hopf Bifurcation and Stochastic Resonance of Electrical Activities in Neuron under Electromagnetic Induction10.3389/fncom.2018.00006 ↗
24. Herd behavior in a predator–prey model with spatial diffusion: Bifurcation analysis and Turing instability10.1007/s12190-017-1137-9 ↗
25. Undamped Oscillations Generated by Hopf Bifurcations in Fractional-Order Recurrent Neural Networks With Caputo Derivative10.1109/TNNLS.2015.2425734 ↗
26. Modeling transmission dynamics of lyme disease: Multiple vectors, seasonality, and vector mobility
27. Spatiotemporal behavior in a predator-prey model with herd behavior and cross-diffusion and fear effect10.1140/epjp/s13360-021-01489-7 ↗
28. Panigoro, H.S., Suryanto, A., Kusumawinahyu, W.M., and Darti, I. (2021). Dynamics of an Eco-Epidemic Predator–Prey Model Involving Fractional Derivatives with Power-Law and Mittag Leffler Kernel. Symmetry, 13.10.3390/sym13050785 ↗
29. Pattern formation of a diffusive predator-prey model with herd behavior and nonlocal prey competition10.1002/mma.6036 ↗
30. Oscillatory Expression of the bHLH Factor Hes1 Regulated by a Negative Feedback Loop10.1126/science.1074560 ↗
31. Genetic oscillation deduced from Hopf bifurcation in a genetic regulatory network with delays10.1016/j.mbs.2008.05.004 ↗