Control of Coexisting Attractors with Preselection of the Survived Attractor in Multistable Chua’s System: A Case Study

Abstract

Although the control of multistability has already been reported, the one with preselection of the desired attractor is still uncovered in systems with more than two coexisting attractors. This work reports the control of coexisting attractors with preselection of the survived attractors in paradigmatic Chua’s system with smooth cubic nonlinearity. Techniques of linear augmentation combined to system invariant parameters like equilibrium points are used to choose the desired surviving attractors among the coexisting ones. Nonlinear dynamical tools including bifurcation diagrams, standard Lyapunov exponents, phase portraits, and cross section of initial conditions are exploited to reveal the selection scenarios of the survived attractor in the multistability control process of Chua’s system. The main crisis towards annihilation of multistability in Chua’s system when varying the coupling strength is interior crisis and border collision. Theoretical and numerical results obtained are further validated with PSpice analysis.

Controling Switching between Birhythmic States in a New Conductance-based Bursting Neuronal Model

“…More importantly, we analytical define the system parameter domain where these many attractors coexist. On the contrary of other models where the coexistence between two periodic regimes (birhythmicity), random oscillations (chaos), and coexistence of a stable limit-cycle oscillations are done numerically [19][20][21], our model offer a room for analytical analysis. Note that, the understanding of the duality (birhythmicity) of neurons has motived many researchers in proposing some models [17,[19][20][21].…”

“…On the contrary of other models where the coexistence between two periodic regimes (birhythmicity), random oscillations (chaos), and coexistence of a stable limit-cycle oscillations are done numerically [19][20][21], our model offer a room for analytical analysis. Note that, the understanding of the duality (birhythmicity) of neurons has motived many researchers in proposing some models [17,[19][20][21]. The faithfulness of these models to underline that biological neuron and it complexity is crucial in describing the information processing and transmission in neuronal system [5].…”

“…These results were founded by Cymbalyuk and Shilnikov [28] and in the three dimensional autonomous ML model [12] but coexisting attractors were in the same amplitude. They were also founded in a simple and chaotic Jerk system [17], in the chua's system [19] and in a Yu-Wang four-Wing chaotic system [20]. By taking some value of the control parameter α, we shows in figure 11 with some phase portrait, the dynamic of the neuron as: a coexistence to period-11 substhreshold oscillations and tonic spiking figure 11 This large amplitude is therefore desirable because it can become more chaotic.…”

Multistability and Its Control by the PWM Carrier Signal Modulation in a DC Electric Drive System

“…Proceeding with the problem of controlling multistability, the diversity of techniques is classifed into two main categories, depending on whether the control (i) drives the system to the desired mode by an external perturbation [45][46][47] or (ii) forces the collapse of the undesired modes [48][49][50]. Te one studied in the work can belong to both categories within the above classifcation (depending on the particular implementation).…”

Coexistence of hyperchaos with chaos and its control in a diode-bridge memristor based MLC circuit with experimental validation

“…Furthermore, such strategies have been demonstrated so far only in the case of bistable systems. Regarding linear augmentation strategy, recent results have generalized the control scheme to systems with up to five coexisting attractors and with possible pre-selection of the survive monostable attractor [43][44][45]. Despite such effort, one major drawback in the control outcome was noticed.…”