Stability analysis and limit cycle in fractional system with Brusselator nonlinearities

The investigation of limit cycles in the fractional dynamical systems with Brusselator nonlinearities is considered. We present analysis of the stability domains as well as possible solutions realizing at different system parameters.

[1]  Changpin Li,et al.  Synchronization in fractional-order differential systems , 2005 .

[2]  Rudolf Gorenflo,et al.  Convergence of the Grünwald-Letnikov scheme for time-fractional diffusion , 2007 .

[3]  Jean-François Deü,et al.  An adaptation of the Gear scheme for fractional derivatives , 2006 .

[4]  V. V. Gafiychuk,et al.  Inhomogeneous oscillatory structures in fractional reaction-diffusion systems , 2008 .

[5]  Elsayed Ahmed,et al.  On some Routh–Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rössler, Chua and Chen systems , 2006 .

[6]  I. Podlubny.  Fractional differential equations , 1998 .

[7]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[8]  E. Ahmed,et al.  Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models , 2007 .

[9]  Mohammad Saleh Tavazoei,et al.  A necessary condition for double scroll attractor existence in fractional-order systems , 2007 .

[10]  V. Gafiychuk,et al.  Stability analysis and oscillatory structures in time-fractional reaction-diffusion systems. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Ivo Petras,et al.  A note on the fractional-order Chua’s system , 2008 .

[12]  V. V. Gafiychuk,et al.  Analysis of fractional order Bonhoeffer–van der Pol oscillator , 2008 .

[13]  Changpin Li,et al.  Does the fractional Brusselator with efficient dimension less than 1 have a limit cycle , 2007 .