Multistability in Piecewise Linear Systems versus Eigenspectra Variation and Round Function

@article{GilardiVelzquez2017MultistabilityIP,
  title={Multistability in Piecewise Linear Systems versus Eigenspectra Variation and Round Function},
  author={H. E. Gilardi-Vel{\'a}zquez and Luis J. Ontanon-Garcia and Germ{\'a}n Rodr{\'i}guez and Eric Campos-Cant{\'o}n},
  journal={Int. J. Bifurc. Chaos},
  year={2017},
  volume={27},
  pages={1730031:1-1730031:14}
}
A multistable system generated by Piecewise Linear (PWL) subsystems based on the jerk equation is presented. The system’s behavior is characterized by means of the Nearest Integer or the round(x) function to control the switching events and to locate the corresponding equilibria on each of the commutation surfaces. These surfaces are generated through the switching function dividing the space into regions equally distributed along one axis. The trajectory of the system is governed by the… 

On multistability behavior of unstable dissipative systems

We present a dissipative system with unstable dynamics called unstable dissipative system which are capable of generating a multi-stable behavior, i.e., depending on its initial condition the

On multistability behavior of unstable dissipative systems.

TLDR
A structure is proposed where both the linear part and the switching function depend on two parameters, and the range of values of such parameters where the PWL system presents a multistable behavior and trajectories with multiscrolls is shown.

Emergence of a square chaotic attractor through the collision of heteroclinic orbits

In this work we introduce a square chaotic attractor based on the collision of two heteroclinic orbits. Before the collision, the system presents the coexistence of two double scroll attractors that

Multistability Emergence through Fractional-Order-Derivatives in a PWL Multi-Scroll System

TLDR
The presented results are not only applicable in engineering fields, but they also enrich the analysis and the understanding of the implications of using fractional integration orders, boosting the development of further and better studies.

Derivation of a continuous time dynamic planar system with two unstable foci from a three-dimensional chaotic piecewise linear system.

TLDR
A class of continuous time dynamical planar systems that is capable of generating attractors in the plane by means of the use of hysteresis and at least two unstable foci is introduced.

Chaos Generated by a Class of 3D Three-Zone Piecewise Affine Systems with Coexisting Singular Cycles

TLDR
This paper proposes some criteria to accurately locate the coexistence of homoclinic cycles and of heteroclini cycles in a class of three-dimensional (3D) piecewise affine systems (PASs), respectively, and establishes the existence conditions of chaos arising from such coexistence.

Predicting Tipping Points in Chaotic Maps with Period-Doubling Bifurcations

TLDR
This paper presents a meta-modelling framework for solving the challenges of complex system optimization and big data processing in the rapidly changing environment.

A novel approach to generate attractors with a high number of scrolls

References

SHOWING 1-10 OF 23 REFERENCES

Multiscroll attractors by switching systems.

TLDR
This paper describes how a piecewise-linear switching system yields multiscroll attractors, symmetric or asymmetric, with chaotic behavior.

Control of multistability

Complex Dynamics in multistable Systems

TLDR
It is shown that multistable systems are very sensitive to perturbations leading to a noise-induced hopping process between attractors and their basins of attraction.

Multistability and hidden attractors in an impulsive Goodwin oscillator with time delay

TLDR
Bifurcation analysis of a hybrid model that attempts to integrate the intermittent bursting activity with a continuous hormone secretion results in a model capable of displaying quasiperiodicity and border collisions as well as multistability and hidden attractors.

Multiple steady states and dissipative structures in a circular and linear array of three cells : numerical and experimental approaches

TLDR
The steady‐state behavior of a circular and linear array of three cells containing a substrate‐inhibited‐like kinetics catalyzed by immobilized thylakoids is studied and three domains of stable stationary behavior are determined.

Attractors generated from switching unstable dissipative systems.

TLDR
A class of 3-D unstable dissipative systems, which are stable in two components but unstable in the other one, which is motivated by whirls, comprised of switching subsystems, which yield strange attractors from the combination of two unstable "one-spiral" trajectories by means of a switching rule.

Controlling bistability by linear augmentation

Transverse laser patterns. I. Phase singularity crystals.

TLDR
The interaction and the competition of a set of transverse cavity modes, which belong to a frequency-degenerate family, are analyzed and the predicted phase singularities in each pattern agree in detail with those found by theory.