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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.

Cyclic Processes And Isolated Systems

Cyclic Processes And Isolated Systems

A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each...

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...

BIBO stability of continuous and discrete -time systems

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....

Linear time-invariant Systems

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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Classification of Systems-I

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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:

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Updated: Sep 22, 2025

A Precise and Autonomous System for the Detection of Insect Emergence Patterns

A Precise and Autonomous System for the Detection of Insect Emergence Patterns

Published on: January 9, 2019

Emergence and algorithmic information dynamics of systems and observers.

Felipe S Abrahão^1,2, Hector Zenil^2,3,4,5

¹National Laboratory for Scientific Computing (LNCC), 25651-075 Petropolis, Rio de Janeiro, Brazil.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|May 23, 2022

Summary

Emergence of algorithmic information is observer-dependent, influenced by formal knowledge. However, rapid information increase leads to asymptotically observer-independent emergence, a robust form across theories.

Keywords:

algorithmic information dynamics dynamical systems emergence observers

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Area of Science:

Complex Systems
Information Theory
Philosophy of Science

Background:

Defining emergence is challenging due to observer subjectivity.
Formalizing observation as mutual perturbations between dynamical systems is key.
Prior knowledge can influence whether a phenomenon appears emergent or reducible.

Purpose of the Study:

To formalize the concept of emergence in relation to the observer.
To differentiate between observer-dependent and observer-independent emergence.
To demonstrate models exhibiting different types of emergence.

Main Methods:

Formalizing observation as mutual perturbations between dynamical systems.
Analyzing the emergence of algorithmic information.
Developing evolutionary and network models to demonstrate emergence variants.

Main Results:

Algorithmic information emergence is observer-dependent regarding formal knowledge.
Observer-dependent emergence (ODE) is robust to other subjective factors like measurement or language.
Unbounded algorithmic information increase implies asymptotically observer-independent emergence (AOIE).
AOIE is robust across different observer theories.
Demonstrated evolutionary (diachronic) and network (holistic) models of AOIE.

Conclusions:

AOIE represents the strongest form of emergence within formal theories for computable systems.
Observer-dependent emergence (ODE) highlights the role of observer's knowledge.
Asymptotically observer-independent emergence (AOIE) offers a more universal definition of emergent phenomena.