Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Second Order systems II

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.

First Order Systems

First Order Systems

First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...

Second Order systems I

Second Order systems I

A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...

Dynamic Equilibrium

Dynamic Equilibrium

A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...

Classification of Systems-I

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:

Classification of Systems-II

Classification of Systems-II

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same journal

Complex network topological and spectral determinants of extreme events.

Chaos (Woodbury, N.Y.)·2026

Same journal

On the role of higher-order interactions toward first synchronization time.

Chaos (Woodbury, N.Y.)·2026

Same journal

Bifurcations and chaotic analysis in a discrete predator-prey model with Ricker map.

Chaos (Woodbury, N.Y.)·2026

Same journal

Dynamical thermalization and turbulence in social stratification models.

Chaos (Woodbury, N.Y.)·2026

Same journal

Endogenous regime switching driven by scalar-irreducible learning dynamics.

Chaos (Woodbury, N.Y.)·2026

Same journal

The coherence analysis and Laplacian spectrum applications of cycle-based iterative networks.

Chaos (Woodbury, N.Y.)·2026

Search research articles

Related Experiment Video

Updated: Jan 22, 2026

Fabrication of Micropatterned Hydrogels for Neural Culture Systems using Dynamic Mask Projection Photolithography

Fabrication of Micropatterned Hydrogels for Neural Culture Systems using Dynamic Mask Projection Photolithography

Published on: February 11, 2011

Shilnikov problem in Filippov dynamical systems.

Douglas D Novaes¹, Marco A Teixeira¹

¹Departamento de Matemática, Universidade Estadual de Campinas, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária Zeferino Vaz, 13083-859 Campinas, SP, Brazil.

Chaos (Woodbury, N.Y.)

|July 4, 2019

Summary

This summary is machine-generated.

This study introduces sliding Shilnikov orbits in 3D Filippov systems, which are unique closed curves that slide on a switching surface. These orbits lead to infinitely many sliding periodic orbits without extra assumptions.

More Related Videos

Author Spotlight: Developing a Unique Modular Microphysiological System to Mimic Human Barrier Tissue

Author Spotlight: Developing a Unique Modular Microphysiological System to Mimic Human Barrier Tissue

Published on: February 16, 2024

Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs

Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs

Published on: August 9, 2024

Related Experiment Videos

Last Updated: Jan 22, 2026

Fabrication of Micropatterned Hydrogels for Neural Culture Systems using Dynamic Mask Projection Photolithography

Fabrication of Micropatterned Hydrogels for Neural Culture Systems using Dynamic Mask Projection Photolithography

Published on: February 11, 2011

Author Spotlight: Developing a Unique Modular Microphysiological System to Mimic Human Barrier Tissue

Author Spotlight: Developing a Unique Modular Microphysiological System to Mimic Human Barrier Tissue

Published on: February 16, 2024

Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs

Author Spotlight: Streamlining Visual Dynamics to Simplify Molecular Dynamics Simulations Using Gromacs

Published on: August 9, 2024

Area of Science:

Dynamical Systems and Control Theory
Nonlinear Dynamics
Differential Equations

Background:

Filippov systems are crucial for modeling discontinuous phenomena.
Shilnikov orbits are known for generating complex dynamics.
The behavior of trajectories on switching surfaces in Filippov systems is not fully understood.

Purpose of the Study:

To introduce and define sliding Shilnikov orbits in 3D Filippov systems.
To investigate the existence and properties of these orbits.
To demonstrate their occurrence in generic systems and discontinuous piecewise linear systems.

Main Methods:

Analysis of Filippov systems using piecewise smooth dynamical system theory.
Adaptation of Shilnikov's theorem for Filippov systems.
Construction of examples exhibiting sliding Shilnikov orbits.

Main Results:

Definition of sliding Shilnikov orbits as closed Filippov trajectories sliding on a switching surface.
Proof of the existence of sliding Shilnikov orbits in generic one-parameter families of Filippov systems.
Demonstration of the existence of infinitely many sliding periodic orbits near a sliding Shilnikov orbit.
Exhibition of sliding Shilnikov orbits in discontinuous piecewise linear differential systems.

Conclusions:

Sliding Shilnikov orbits represent a novel phenomenon in Filippov systems.
These orbits are robust and occur generically.
The findings expand the understanding of complex dynamics in discontinuous systems.