Complex Dynamics in Basic Two-Component Auto-Oscillation Systems with Fractional Derivatives of Different Orders
On the basis of simple two-component nonlinear incommensurate fractional-order systems with positive and negative feedbacks, some general properties of fractional auto-oscillation systems are established. By linear stability analysis and numerical simulation, it is shown that fractional derivative orders and ratio between them can substantially change the stability conditions of the system and lead to appearing of complex oscillations and attractors, which cannot be found in their integer counterparts.
KeywordsFractional dynamics Nonlinear system Differential equation
- 5.Tarasov, V.: Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. Springer, Heidelberg (2011)Google Scholar
- 23.Kerner, B.S., Osipov, V.V.: Stochastic inhomogeneous structures in nonequilibrium systems. JETP 52, 1122–1132 (1980). 1980JETP...52.1122KGoogle Scholar
- 26.Matignon, D.: Stability results for fractional differential equations with applications to control processing. Comput. Eng. Syst. Appl. 2, 963–970 (1996). 10.1.1.40.4859Google Scholar