Dynamical States in a Ring of Four Mutually Coupled Self-Sustained Electrical Systems with Time Periodic Coupling

We investigate in this Letter different dynamical states in the ring of four mutually coupled self-sustained electrical systems with time periodic coupling. The transition boundaries that can occur between instability and complete synchronization states when the coupling strength varies are derived using the Floquet theory and the Whittaker method. The effects of the amplitude of the periodic parametric perturbations of the coupling parameter on the stability boundaries are analyzed. Numerical simulations are then performed to complement the analytical results.

[1]  Carroll,et al.  Synchronous chaos in coupled oscillator systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  C. Hayashi,et al.  Nonlinear oscillations in physical systems , 1987 .

[3]  V N Belykh,et al.  Cluster synchronization modes in an ensemble of coupled chaotic oscillators. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  P Woafo,et al.  Generalized correlated states in a ring of coupled nonlinear oscillators with a local injection. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  P Woafo,et al.  Synchronized states in a ring of mutually coupled self-sustained electrical oscillators. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  K. Fukui,et al.  Power Combining Ladder Network with Many Active Devices , 1980 .

[7]  Subhash C. Sinha,et al.  Symbolic Computation of Local Stability and Bifurcation Surfaces for Nonlinear Time-Periodic Systems , 1998 .

[8]  S. Nogi,et al.  Mode Analytical Study of Cylindrical Cavity Power Combiners , 1986 .

[9]  Dmytro M. Vavriv,et al.  Interaction of low- and high-frequency oscillations in a nonlinear RLC circuit , 1994 .

[10]  Chacón.  Suppression of chaos by selective resonant parametric perturbations. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  P. Woafo,et al.  Transitions from spatiotemporal chaos to cluster and complete synchronization states in a shift-invariant set of coupled nonlinear oscillators. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Paul Woafo,et al.  Synchronized states in a ring of four mutually coupled self-sustained electromechanical devices , 2006 .

[13]  Paul Woafo,et al.  Dynamics and synchronization of coupled self-sustained electromechanical devices , 2005 .

[14]  Derek A. Linkens,et al.  Mathematical Modeling of the Colorectal Myoelectrical Activity in Humans , 1976, IEEE Transactions on Biomedical Engineering.

[15]  Lima,et al.  Suppression of chaos by resonant parametric perturbations. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[16]  D. A. Linkens,et al.  A mathematical model of the slow-wave electrical activity of the human small intestine , 1974, Medical and biological engineering.

[17]  Carroll,et al.  Short wavelength bifurcations and size instabilities in coupled oscillator systems. , 1995, Physical review letters.

[18]  Giocondo,et al.  Experimental evidence of suppression of chaos by resonant parametric perturbations. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[19]  Fronzoni,et al.  Effects of parametric perturbations on the onset of chaos in the Josephson-junction model: Theory and analog experiments. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[20]  Tetsuro Endo,et al.  Mode analysis of a ring of a large number of mutually coupled van der Pol oscillators , 1978 .

[21]  Grebogi,et al.  Spatiotemporal dynamics in a dispersively coupled chain of nonlinear oscillators. , 1989, Physical review. A, General physics.