Sil'nikov chaos of the Liu system

Liangqiang Zhou1, Fangqi Chen

  • 1Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People's Republic of China.

Related Concept Videos

Internal Combustion Engine01:20

Internal Combustion Engine

The internal combustion engine is a heat engine that uses the byproducts of combustion as the working fluid instead of using a heat transfer medium to transfer heat. The combustion is done in a way that produces high-pressure combustion products that can be expanded through a turbine or piston to create work. Internal combustion engines can again be categorized into three kinds: (1) spark ignition gasoline engines, most commonly used in automobiles, (2) compression ignition diesel engines that...
Second Order systems II01:18

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.
If  ζ...
Second Order systems I01:20

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...
First Order Systems01:21

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...
Multimachine Stability01:25

Multimachine Stability

Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by: