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A sinusoidally-driven conservative and dissipative system with signum nonlinearity is presented in this paper. The proposed system exhibits strange attractors, multistability, and megastability. The system exhibits both conservative and dissipative behaviors with the change of its parameters. The Lyapunov exponents, Lyapunov spectrum plots, bifurcation diagrams, and phase plots are used to show the special features of the proposed system.

In this paper, a new two-dimensional nonlinear oscillator with an unusual sequence of rational and irrational parameters is introduced. This oscillator has endless coexisting limit cycles, which make it a megastable dynamical system. By periodically forcing this system, a new system is designed which is capable of exhibiting an infinite number of coexisting asymmetric torus and strange attractors. This system is implemented by an analog circuit, and its Hamiltonian energy is calculated.

Recently, chaotic systems with hidden attractors and multistability have been of great interest in the field of chaos and nonlinear dynamics. Two special categories of systems with multistability are systems with extreme multistability and systems with megastability. In this paper, the simplest (yet) megastable chaotic oscillator is designed and introduced. Dynamical properties of this new system are completely investigated through tools like bifurcation diagram, Lyapunov exponents, and basin of attraction. It is shown that between its countable infinite coexisting attractors, only one is self-excited and the rest are hidden.

Multistability is an essential topic in nonlinear dynamics. Recently, two critical subsets of multistable systems have been introduced: systems with extreme multistability and systems with megastability. In this paper, based on a newly introduced megastable system, a megastable forced oscillator is introduced. The effect of adding a forcing term and its parameters on the dynamical behavior of the designed system is investigated. By the help of bifurcation diagram and Lyapunov exponents, it is shown that the modified oscillator can show a variety of dynamical solutions including limit cycle, torus, and strange attractor.

In the last two years, many chaotic or hyperchaotic systems with megastability have been reported in the literature. The reported systems with megastability are mostly developed from their dynamic equations without any reference to the physical systems. In this paper, the dynamics of a single-link manipulator is considered to observe the existence of interesting dynamical behaviors. When the considered dynamical system is excited with (a) periodically forced input or (b) quasi-periodically forced input, it indicates the existence of megastability. This paper reports megastability in a physical dynamical system with infinitely many equilibria. The considered system has other dynamical behaviors like chaotic, quasi-periodic and periodic. These behaviors are analyzed using Lyapunov spectrum, bifurcation diagram and phase plots. The simulation results reveal that the objectives of the paper are achieved successfully.

The simplest megastable chaotic system is built by employing a piecewise-linear damping function which is periodic over the spatial domain. The unforced oscillator generates an infinite number of nested limit cycles with constant distances whose strength of attraction decreases gradually as moving to outer ones. The attractors and the basins of attraction of the proposed system are almost compatible with those of the system with sinusoidal damping. However, the nonzero Lyapunov Exponent of the latter is consistently below that of the former. A comparative bifurcation analysis is carried out for periodically forced systems, showing the chaotic behavior of coexisting attractors in specific values of parameters. Changing the bifurcation parameter results in expansion, contraction, merging, and separation of the coexisting attractors, make it challenging to find the corresponding basins. Three symmetric pairs of attractors are observed; each one consists of two symmetric attractors (with respect to the origin) with almost the same values of the corresponding Lyapunov Exponent.

Benefiting from trigonometric and hyperbolic functions, a nonlinear megastable chaotic system is reported in this paper. Its nonlinear equations without linear terms make the system dynamics much more complex. Its coexisting attractors’ shape is diamond-like; thus, this system is said to have diamond-shaped oscillators. State space and time series plots show the existence of coexisting chaotic attractors. The autonomous version of this system was studied previously. Inspired by the former work and applying a forcing term to this system, its dynamics are studied. All forcing term parameters’ impacts are investigated alongside the initial condition-dependent behaviors to confirm the system’s megastability. The dynamical analysis utilizes one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents, Kaplan–Yorke dimension, and attraction basin. Because of this system’s megastability, the one-dimensional bifurcation diagrams and Kaplan–Yorke dimension are plotted with three distinct initial conditions. Its analog circuit is simulated in the OrCAD environment to confirm the numerical simulations’ correctness.