Hopf Bifurcation Analysis for the Comprehensive National Strength Model with Time Delay
Abstract
This paper mainly modifies and further develops the comprehensive national strength model. By modifying the basic comprehensive national strength model, it can more accurately illustrate the society phenomena with time delay. First, we research the dynamics of the modified with time delay. By employing the normal form theory and center manifold method, we obtain some testable results on these issues. The conclusion confirms that a Hopf bifurcation occurs due to the existence of stability switches when the delay varies. Finally, some numerical simulations are given to illustrate the effectiveness of our result.
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Conclusion
These papers apply delay in the comprehensive national strength model, which show rich dynamics behavior. Different from previous studies, we added the influence of time delay feedback in the system (1.3). Dynamic behavior of comprehensive national strength model with time delay is analyzed by using the method of quantitative. When delay $\tau$ across a series of critical value, nonlinear dynamic system generate the Hopf bifurcation. In addition, by employing the normal form theory and center manifold method, we obtain some testable results on these issues. We use normative theory and center of popular theorem obtained the calculating method of the direction of Hopf bifurcation and stability of periodic solutions. Finally, the above theoretical analysis is verified by numerical simulation. The dynamic behavior of the comprehensive national strength model is rich. Many aspects is not mining, yet to be. References