Cover Image

From two-dimensional continuous maps to one-dimensional discontinuous maps: a novel reduction explaining complex bifurcation structures in piecewise-linear families of maps

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Simpson, D. J. W., Avrutin, V.
Format:	Preprint
Published:	2025
Subjects:	Dynamical Systems Chaotic Dynamics 39A28, 37G25, 37G35
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

The two-dimensional border-collision normal form with a zero determinant
by: Simpson, David J. W.
Published: (2024)

Further results for a family of continuous piecewise linear planar maps
by: Cima, Anna, et al.
Published: (2025)

Three forms of dimension reduction for border-collision bifurcations
by: Simpson, David J. W.
Published: (2024)

Boundary Hopf bifurcations in three-dimensional Filippov systems
by: Simpson, David J. W.
Published: (2026)

Robust chaos in $\mathbb{R}^n$
by: Ghosh, Indranil, et al.
Published: (2024)

Extended normal forms for one-dimensional border-collision bifurcations
by: Glendinning, P. A., et al.
Published: (2024)

Resonant grazing bifurcations revisited
by: Simpson, David J. W., et al.
Published: (2026)

Nonsmooth bifurcations in families of one-dimensional piecewise-linear quasiperiodically forced maps
by: Martinez-Vergara, Rafael, et al.
Published: (2025)

Dynamical analysis of r-Chialvo neuron map with cosine memristive
by: Kumar, Ajay, et al.
Published: (2026)

Invariant graphs and dynamics of a family of continuous piecewise linear planar maps
by: Cima, Anna, et al.
Published: (2024)

Complex transitions between spiking, bursting and silent regimes in a new memristive Rulkov neuronal model
by: Moreno, Miguel, et al.
Published: (2026)

A degenerate Takens--Bogdanov bifurcation in a normal form of Lorenz's equations
by: Algaba, A., et al.
Published: (2025)

A piecewise-linear fixed point theorem
by: Simpson, David J. W.
Published: (2024)

The bifurcation structure within robust chaos for two-dimensional piecewise-linear maps
by: Ghosh, Indranil, et al.
Published: (2024)

Thermodynamic formalism for piecewise expanding maps in finite dimension
by: Baladi, Viviane, et al.
Published: (2023)

Bifurcation analysis of multiple limit cycles created in boundary equilibrium bifurcations in hybrid systems
by: Tang, Hong, et al.
Published: (2024)

Multifractal analysis of intermingled basins and blowout bifurcations in a parametetric family of skew product maps
by: Ghane, Fatemeh Helen, et al.
Published: (2025)

Asymptotically periodic and bifurcation points in fractional difference maps
by: Edelman, Mark
Published: (2024)

On distinguishing genuine from spurious chaos in planar singular and nonsmooth systems: A diagnostic approach
by: Ramírez, Martha Alvarez
Published: (2026)

Multiple Local and Global Bifurcations and Their Role in Quorum Sensing Dynamics
by: Harris, Mariana, et al.
Published: (2024)

Bistability and chaos in the discrete two-gene Andrecut-Kauffman model
by: Rosman, Mikołaj, et al.
Published: (2024)

Asymmetric Duffing oscillator: metamorphoses of $1:2$ resonance and its interaction with the primary resonance
by: Kyziol, Jan, et al.
Published: (2024)

Generic one-parameter families of 3-dimensional Filippov Systems
by: Euzébio, R. D., et al.
Published: (2026)

Resonance properties and chaotic dynamics of a three-dimensional discrete logistic ecological system within the neighborhoods of bifurcation points
by: Chen, Yujiang, et al.
Published: (2025)

Chaotic discretization theorems for forced linear and nonlinear coupled oscillators
by: Disca, Stefano, et al.
Published: (2025)

Bifurcations in periodic integrodifference equations in $C(Ω)$ I: Analytical results and applications
by: Aarset, Christian, et al.
Published: (2020)

On some rational piecewise linear rotations
by: Cima, Anna, et al.
Published: (2023)

Continuation and bifurcations of periodic orbits and symbolic dynamics in the Swift-Hohenberg equation
by: Czwórnóg, Jakub, et al.
Published: (2024)

An improved approach for estimating the dimension of inertial manifolds in chaotic distributed dynamical systems via analysis of angles between tangent subspaces
by: Kuptsov, Pavel V.
Published: (2025)

Structure analysis of the Lorenz-84 chaotic attractor
by: Rosalie, Martin, et al.
Published: (2025)

Finite-Time Analysis of Crises in a Chaotically Forced Ocean Model
by: Axelsen, Andrew R., et al.
Published: (2023)

Asymptotic cycles in fractional generalizations of multidimensional maps
by: Edelman, Mark
Published: (2024)

Heterodimensional cycles derived from homoclinic tangencies via Hopf bifurcations
by: Tomizawa, Shuntaro
Published: (2025)

Chenciner bifurcation, strong resonances and Arnold tongues of a discrete time SIR epidemic model
by: Yu, Jiangqiong, et al.
Published: (2025)

Astrocytes: Arnol'd Tongues Generalization in Dynamical Systems' Parameter Plane
by: Ramírez-Ávila, Gonzalo Marcelo, et al.
Published: (2026)

Singular bifurcations in a modified Leslie-Gower model
by: García, Roberto Albarran, et al.
Published: (2024)

Concave-convex nonautonomous scalar ordinary differential equations: from bifurcation theory to critical transitions
by: Dueñas, Jesús, et al.
Published: (2024)

Global bifurcation diagrams for coercive third-degree polynomial ordinary differential equations with recurrent nonautonomous coefficients
by: Elia, Cinzia, et al.
Published: (2025)

Quasi-compactness and statistical properties for discontinuous systems semi-conjugate to piecewise convex maps with countably many branches
by: Lucena, Rafael
Published: (2025)

Regular and chaotic Welander oscillations in a four-dimensional conceptual model for the Atlantic Meridional Overturning Circulation
by: Bailie, John, et al.
Published: (2026)