Abstract
This review paper describes different lumped circuitry realizations of the chaotic dynamical systems having equilibrium degeneration into a plane object with topological dimension of the equilibrium structure equals one. This property has limited amount (but still increasing, especially recently) of third-order autonomous deterministic dynamical systems. Mathematical models are generalized into classes to design analog networks as universal as possible, capable of modeling the rich scale of associated dynamics including the so-called chaos. Reference state trajectories for the chaotic attractors are generated via numerical analysis. Since used active devices can be precisely approximated by using third-level frequency dependent model, it is believed that computer simulations are close enough to capture real behavior. These simulations are included to demonstrate the existence of chaotic motion.
Highlights
Di®erent congurations of lumped analog circuits capable of modeling continuous chaotic dynamics attract signicant interest of researchers and engineers for the lastJ
The main aim of this paper is to address the question if the chaotic dynamics with a nonconventional equilibrium formation can be implemented as hybrid-mode or the fully current-mode electronic circuits
Numerical studies reveal that the global behavior of this dynamical system is extremely sensitive to both radiuses and chaos quickly disappears for values far away from unity; a solution became unbounded leading to the state space attractor limited only by the saturation levels of the used active devices
Summary
Di®erent congurations of lumped analog circuits capable of modeling continuous chaotic dynamics attract signicant interest of researchers and engineers for the last. Mathematical model with chaotic behavior and equilibrium in the form of surface objects such as one or several lines (two parallel),[45,46,47] hyperbola,[48] circle[49] and ellipse, square,[50] other conic-sectioned equilibrium[51] or a general curve equilibrium.[52,53,54] it seems that only a portion of line, circle or square is responsible for chaos generation Based on these recent discoveries in theeld of nonlinear dynamic theory, it is not a breathtaking fact that 3D equilibrium structure such as cube can lead to the evolution of chaos.[55] Systematic procedure towards the chaotic dynamics with any number of equilibria is described in Ref. 56. Simplicity of models predestinates them for the circuit realizations dedicated for various exhibitions, educational or basic research purposes (for example, bifurcation sequences can be traced and captured)
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