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Everything about Initial condition

Parameter in differential equations and dynamical systems

In mathematics and particularly in dynamical systems, an initial condition is the initial value of a differential equation, difference equation, or other "time"-dependent equation which evolves in time. The most fundamental case, an ordinary differential equation of order k, generally requires k initial conditions to trace the equation's evolution through time. In other contexts, the term may refer to an initial value of a recurrence relation, discrete dynamical system, hyperbolic partial differential equation, or even a seed value of a pseudorandom number generator, at "time zero", enough such that the overall system can be evolved in "time", which may be discrete or continuous. The problem of determining a system's evolution from initial conditions is referred to as an initial value problem. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Initial conditionA 5-minute orientation
  2. Skim a recent paper: A New Look at the Initial Condition ProblemInfluential work since 2022
  3. Pick up a classic book: Reading Lolita in TehranThe most-reprinted book on the subject
  4. Read the landmark paper: Initial conditions and moment restrictions in dynamic panel data modelsCited 20,547 times
  5. Go sideways: Linear dynamical systemA closely related topic
  6. Go sideways: Flow (mathematics)A closely related topic

📖 Definitions

Noun In dynamical system, an initial condition is the value of a variable at a specific time, also known as a seed value.

🗂️ The subject at a glance

  1. Linear system
  2. Nonlinear systems
  3. Empirical laws and initial conditions

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

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