In this paper, the classical Lorenz model is under investigation, in which a periodic heating term replaces the constant one. Applying the variable heating term causes time-dependent behaviors in the Lorenz model. The time series produced by this model are chaotic; however, they have fixed point or periodic-like qualities in some time intervals. The energy dissipation and equilibrium points are examined comprehensively. This modified Lorenz system can demonstrate multiple kinds of coexisting attractors by changing its initial conditions and, thus, is a multi-stable system. Because of multi-stability, the bifurcation diagrams are plotted with three different methods, and the dynamical analysis is completed by studying the Lyapunov exponents and Kaplan-Yorke dimension diagrams. Also, the attraction basin of the modified system is investigated, which approves the appearance of coexisting attractors in this system.
Extreme multistable systems can show vibrant dynamical properties and infinitely many coexisting attractors generated by changing the initial conditions while the system and its parameters remain unchanged. On the other hand, the frequency of extreme events in society is increasing which could have a catastrophic influence on human life worldwide. Thus, complex systems that can model such behaviors are very significant in order to avoid or control various extreme events. Also, hidden attractors are a crucial issue in nonlinear dynamics since they cannot be located and recognized with conventional methods. Hence, finding such systems is a vital task. This paper proposes a novel five-dimensional autonomous chaotic system with a line of equilibria, which generates hidden attractors. Furthermore, this system can exhibit extreme multistability and extreme events simultaneously. The fascinating features of this system are examined by dynamical analysis tools such as Poincaré sections, connecting curves, bifurcation diagrams, Lyapunov exponents spectra, and attraction basins. Moreover, the reliability of the introduced system is confirmed through analog electrical circuit design so that this chaotic circuit can be employed in many engineering fields.
This paper introduces a new 3D conservative chaotic system. The oscillator preserves the energy over time, according to the Kaplan–Yorke dimension computation. It has a line of unstable equilibrium points that are investigated with the help of eigenvalues and also numerical analysis. The bifurcation diagrams and the corresponding Lyapunov exponents show various behaviors, for example, chaos, limit cycle, and torus with different parameters. Other dynamical properties, such as Poincaré section and basin of attraction, are investigated. Additionally, an oscillator’s electrical circuit is designed and implemented to demonstrate its potentiality.
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