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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.

A new 4D memristive chaotic system with an infinite number of equilibria is proposed via exhaustive computer search. Interestingly, such a new memristive system has a plane of equilibria and two other lines of equilibria. Lyapunov exponent and bifurcation analysis show that this system has chaotic solutions with coexisting attractors. The basins of attraction of the coexisting attractors show chaos, stable fixed-points, and unbounded solutions. Furthermore, the 2D parameter space of the system is explored to find the optimum values of the parameters using the ALO (Ant Lion Optimizer) optimization algorithm.