We analytically demonstrate that temporal modulational instability of pulse combined with discret... more We analytically demonstrate that temporal modulational instability of pulse combined with discrete effects in an array of optical fibers in regime of anomalous dispersion can generate secondary excitations in the gap. These excitations are bound closely to the perturbations of the soliton propagating in the array. They can be of any nature or soliton type and disappear when the modulational instability vanishes. This approach in the research of gap solitons being new, necessitates finding an appropriated method in the research of gap solitons. So the Bogning-Djeumen Tchaho-Kofané method used in this context seems better adapted to determine the analytical shape of gap soliton.
A linear resistive-capacitive-inductance shunted junction (LRCLSJ) model obtained by replacing th... more A linear resistive-capacitive-inductance shunted junction (LRCLSJ) model obtained by replacing the nonlinear piecewise resistance of a nonlinear resistive-capacitive-inductance shunted junction (NRCLSJ) model by a linear resistance is analyzed in this paper. The LRCLSJ model has two or no equilibrium points depending on the dc bias current. For a suitable choice of the parameters, the LRCLSJ model without equilibrium point can exhibit regular and fast spiking, intrinsic and periodic bursting, and periodic and chaotic behaviors. We show that the LRCLSJ model displays similar dynamical behaviors as the NRCLSJ model. Moreover the coexistence between periodic and chaotic attractors is found in the LRCLSJ model for specific parameters. The lowest order of the commensurate form of the no equilibrium LRCLSJ model to exhibit chaotic behavior is found to be 2.934. Moreover, adaptive finite-time synchronization with parameter estimation is applied to achieve synchronization of unidirectional ...
We analytically demonstrate that temporal modulational instability of pulse combined with discret... more We analytically demonstrate that temporal modulational instability of pulse combined with discrete effects in an array of optical fibers in regime of anomalous dispersion can generate secondary excitations in the gap. These excitations are bound closely to the perturbations of the soliton propagating in the array. They can be of any nature or soliton type and disappear when the modulational instability vanishes. This approach in the research of gap solitons being new, necessitates finding an appropriated method in the research of gap solitons. So the Bogning-Djeumen Tchaho-Kofané method used in this context seems better adapted to determine the analytical shape of gap soliton.
A linear resistive-capacitive-inductance shunted junction (LRCLSJ) model obtained by replacing th... more A linear resistive-capacitive-inductance shunted junction (LRCLSJ) model obtained by replacing the nonlinear piecewise resistance of a nonlinear resistive-capacitive-inductance shunted junction (NRCLSJ) model by a linear resistance is analyzed in this paper. The LRCLSJ model has two or no equilibrium points depending on the dc bias current. For a suitable choice of the parameters, the LRCLSJ model without equilibrium point can exhibit regular and fast spiking, intrinsic and periodic bursting, and periodic and chaotic behaviors. We show that the LRCLSJ model displays similar dynamical behaviors as the NRCLSJ model. Moreover the coexistence between periodic and chaotic attractors is found in the LRCLSJ model for specific parameters. The lowest order of the commensurate form of the no equilibrium LRCLSJ model to exhibit chaotic behavior is found to be 2.934. Moreover, adaptive finite-time synchronization with parameter estimation is applied to achieve synchronization of unidirectional ...
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