Hopf bifurcation for a class of fractional differential equations with delay
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The main purpose of this manuscript is to prove the existence of solutions for delay fractional order differential equations (FDE) at the neighborhood of its equilibrium point. After we convert the delay FDE into linear delay FDE by using its equilibrium point, we define the 1:2 resonant double Hopf point set with its characteristic equation. We find the members of this set in different cases. The bifurcation curves for a class of delay FDE are obtained within a differential operator of Caputo type with the lower terminal at −∞.
KeywordsFractional calculus Hopf bifurcation
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- 7.Magin, R.L.: Fractional Calculus in Bioengineering. Begell House Publisher, Inc., Reading (2006) Google Scholar
- 17.Izhikevich, E.M.: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. MIT Press, Cambridge (2007) Google Scholar
- 20.Izhikevich, E.M.: Dynamical Systems in Neuroscience. MIT Press, Cambridge (2007) Google Scholar
- 21.Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Springer, New York (2006) Google Scholar