A non-autonomous mega-extreme multistable chaotic system

Ahmadi, Atefeh; Parthasarathy, Sriram; Natiq, Hayder; Jafari, Sajad; Franović, Igor; Rajagopal, Karthikeyan

doi:10.1016/j.chaos.2023.113765

Cited by 12 publications

(3 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, for f = 0.01 and ω = 0.9, two periodic responses coexist; the amplitude of the periodic response in the upper solution branch is much higher than the one in the lower solution branch. As can be calculated from Equation (26) and observed from the red solution branch of Figure 4a, the natural frequency ω ≈ 1.09. In Figure 4a, the numerical results coincide well with the analytical results, except for the left side of the SN bifurcation points.…”

Section: Periodic Responses Near Each Nontrivial Equilibrium Pointmentioning

confidence: 63%

“…According to the above-mentioned literature, complex dynamical behaviors such as multi-stability [23,24] and chaotic oscillation [25,26] commonly occur in oscillatory systems with strong irrational nonlinearities. Among these dynamical behaviors, higheramplitude or large-extent inter-well responses are more desirable due to their engineering applications in kinematic energy harvesting and vibrating isolation [27].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Global Dynamics and Bifurcations of an Oscillator with Symmetric Irrational Nonlinearities

Liu,

Shang

2023

Fractal Fract

View full text Add to dashboard Cite

This study’s objective is an irrationally nonlinear oscillating system, whose bifurcations and consequent multi-stability under the circumstances of single potential well and double potential wells are investigated in detail to further reveal the mechanism of the transition of resonance and its utilization. First, static bifurcations of its nondimensional system are discussed. It is found that variations of two structural parameters can induce different numbers and natures of potential wells. Next, the cases of mono-potential wells and double wells are explored. The forms and stabilities of the resonant responses within each potential well and the inter-well resonant responses are discussed via different theoretical methods. The results show that the natural frequencies and trends of frequency responses in the cases of mono- and double-potential wells are totally different; as a result of the saddle-node bifurcations of resonant solutions, raising the excitation level or frequency can lead to the coexistence of bistable responses within each well and cause an inter-well periodic response. Moreover, in addition to verifying the accuracy of the theoretical prediction, numerical results considering the disturbance of initial conditions are presented to detect complicated dynamical behaviors such as jump between coexisting resonant responses, intra-well period-two responses and chaos. The results herein provide a theoretical foundation for designing and utilizing the multi-stable behaviors of irrationally nonlinear oscillators.

show abstract

Section: Periodic Responses Near Each Nontrivial Equilibrium Pointmentioning

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Global Dynamics and Bifurcations of an Oscillator with Symmetric Irrational Nonlinearities

Liu,

Shang

2023

Fractal Fract

View full text Add to dashboard Cite

show abstract

“…Bao et al proposed coexisting asymmetric bursters induced by AC in the improved Hindmarsh-Rose model [17]. A novel three-dimensional non-autonomous system exhibiting extreme and mega-stability was crafted by Sajad et al which demonstrated extreme sensitivity against variations in initial conditions about two distinct state variables [18]. Akif et al observed complex dynamical evolution in a chaotic oscillator, including multistability and chaos synchronization [19].…”

Section: Introductionmentioning

confidence: 99%

A memristive chaotic system with two dimensional offset boosting and extreme multistability

Li,

Cai,

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

Due to its unique nonlinearity and memory characteristics, memristor is considered one of the most promising partners for designing chaotic systems. In this paper, a memristor is introduced into a nonlinear system to produce complex dynamical behaviors. Symmetric extremely multistability induced by the initial condition of the memristor is observed in the asymmetric system. Attractors are arranged in the phase space by two independent offset boosters, strength cancellation gives birth to various offset boosting patterns. The effective action of the offset controller is reflected in the linear growth of the mean values and the linear shift of the signal diagrams. Moreover, the circuit implementation based on Multisim demonstrates consistency with numerical simulations and theoretical analyses. Finally, the Pseudorandom Number Generator (PRNG), tested through NIST, is developed to validate its high performance in engineering applications.

show abstract

Exploring extreme multistability in cyclic symmetric conservative systems via two distinct methods

Zhang,

Huang,

Liu

et al. 2024

Nonlinear Dyn

View full text Add to dashboard Cite

A non-autonomous mega-extreme multistable chaotic system

Cited by 12 publications

References 35 publications

Global Dynamics and Bifurcations of an Oscillator with Symmetric Irrational Nonlinearities

Global Dynamics and Bifurcations of an Oscillator with Symmetric Irrational Nonlinearities

A memristive chaotic system with two dimensional offset boosting and extreme multistability

Exploring extreme multistability in cyclic symmetric conservative systems via two distinct methods

Contact Info

Product

Resources

About