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We consider a modified Noguchi electrical transmission line and examine the effects of a linear capacitance C(s) on the wave characteristics while considering the semidiscrete approximation. It appears that wave modulations in the network are governed by a dispersive nonlinear Schrödinger equation whose coefficients are shown to be a function of C(s). We show that the use of this linear capacitance makes the filter more selective. We also show that the width of the unstable regions increases while that of the stable regions decreases with C(s) adding consequently the width of the frequency domain where bright solitons exist. Furthermore, we establish the existence of one more region (compared to the work of Marquié et al. [Marquié et al., Phys. Rev. E 49, 828 (1994)]) in the dispersion curve that allows the motion of envelope solitons of higher frequency in the system. Numerical and experimental investigations done on the model confirm our analytical predictions.

Multistability analysis has received intensive attention in recently, however, its control in systems with more than two coexisting attractors are still to be discovered. This paper reports numerically the multistability control of five disconnected attractors in a self-excited simplified hyperchaotic canonical Chua’s oscillator (hereafter referred to as SHCCO) using a linear augmentation scheme. Such a method is appropriate in the case where system parameters are inaccessible. The five distinct attractors are uncovered through the combination of hysteresis and parallel bifurcation techniques. The effectiveness of the applied control scheme is revealed through the nonlinear dynamical tools including bifurcation diagrams, Lyapunov’s exponent spectrum, phase portraits and a cross section basin of attractions. The results of such numerical investigations revealed that the asymmetric pair of chaotic and periodic attractors which were coexisting with the symmetric periodic one in the SHCCO are progressively annihilated as the coupling parameter is increasing. Monostability is achieved in the system through three main crises. First, the two asymmetric periodic attractors are annihilated through an interior crisis after which only three attractors survive in the system. Then, comes a boundary crisis which leads to the disappearance of the symmetric attractor in the system. Finally, through a symmetry restoring crisis, a unique symmetric attractor is obtained for higher values of the control parameter and the system is now monostable.

This paper investigates the control of multistability in a self-excited memristive hyperchaotic oscillator using linear augmentation method. Such a method is advantageous in the case of system parameters that are inaccessible. The effectiveness of the applied control scheme is revealed numerically through the nonlinear dynamical tools including bifurcation diagrams, Lyapunov exponent spectrum, phase portraits, basins of attraction and relative basin sizes. Results of such numerical methods reveal that the asymmetric pair of chaotic attractors which were coexisting with the symmetric periodic one in the system, are progressively annihilated as the coupling parameter is increasing. The main transitions observed in the control system are the coexistence of three distinct attractors for weak values of the coupling strength. Above a certain critical value of the coupling parameter, only two attractors are now coexisting within the system. Finally, for higher values of the control strength, the controlled system becomes regular and monostable.