dependent on initial conditions

USAGE SUMMARY

The phrase "dependent on initial conditions" is correct and usable in written English.
It can be used in contexts discussing systems, theories, or phenomena that rely on specific starting points or parameters. Example: "The outcome of the experiment was highly dependent on initial conditions, leading to varying results across trials."

✓ Grammatically correct

Science

Academia

News & Media

Human-verified examples from authoritative sources

Exact Expressions

16 human-written examples

(Another definition, if knowledge obeys a margin for error principle, would be: a system exhibits apparent dependence on initial conditions if, for all we know, it is sensitively dependent on initial conditions).

SEP

Fast, but very dependent on initial conditions; known to fail in complex cases with poor initial parameter values.

Harvard University

The system response is found to be strongly dependent on initial conditions.

Journal of Sound and Vibration

Our findings support the notion that the overall growth of the RT mixing is strongly dependent on initial conditions.

International Journal of Heat and Mass Transfer

This makes contrasting estuarine dimensions and development largely dependent on initial conditions, boundary conditions and internal biogeomorphological processes.

Earth-Science Reviews

However, it is necessary to identify patterns that are not dependent on initial conditions, because small scale initial conditions will not normally be measured at large scales.

Ecological Modelling

Human-verified similar examples from authoritative sources

Similar Expressions

44 human-written examples

Apparent dependence on initial conditions can obtain even if sensitive dependence on initial conditions does not.

SEP

F has sensitive dependence on initial conditions.  .

Journal of Inequalities and Applications

Here, the chosen option depends on initial conditions.

Plosone

Whether or not malaria will remain endemic or die out under parameters consistent with disease extinction is dependent both on R 0 and on initial conditions.

BMC Infectious Diseases

It describes the behaviour of dynamic systems that are sensitively dependent on their initial conditions.

The Guardian

Expert writing Tips

Best practice

When describing scientific models or simulations, clearly state that results are "dependent on initial conditions" to indicate potential variability and the importance of precise starting values.

Common error

Avoid assuming that a system's behavior will always be the same regardless of initial conditions. If the system is "dependent on initial conditions", acknowledge that different starting points can lead to significantly different outcomes.

Linguistic Context

The phrase "dependent on initial conditions" functions as a qualifier, specifying that the behavior or outcome of a system or process is contingent upon its starting state. Ludwig AI confirms its usage is correct.

Expression frequency: Uncommon

Frequent in

Science

75%

Academia

15%

News & Media

10%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "dependent on initial conditions" is a grammatically sound and accepted qualifier, primarily used in scientific and academic contexts. As Ludwig AI confirms, it describes systems where small changes in starting conditions can significantly alter outcomes. When writing, it's best to use this phrase to emphasize the importance of accurately defining initial states in models and simulations. Be aware that overgeneralizing a system's behavior without acknowledging the role of initial conditions can lead to inaccurate representations.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

sensitive to starting conditions

Emphasizes the sensitivity or vulnerability of a system to its beginning state.

contingent on initial state

Highlights that the outcome is conditional based on the original state.

reliant on starting parameters

Focuses on the reliance of a process on its initial parameters.

determined by initial circumstances

Stresses that the initial conditions are the cause of the final outcome.

influenced by initial factors

Suggests a weaker, but still significant, impact of starting factors.

governed by seed conditions

Implies that the initial conditions set the rules for what can happen.

predicated on original setup

Indicates that the outcome is fundamentally based on how things began.

shaped by early environment

Highlights the formative role of the initial environment.

conditional on base parameters

States that the final form depends on underlying base parameters.

subject to original settings

Denotes that the process is at the whim of initial configuration.

FAQs

How can I use "dependent on initial conditions" in a sentence?

You can use "dependent on initial conditions" to describe systems where slight changes in the starting state can lead to dramatically different outcomes, such as, "The model's predictions are highly dependent on initial conditions".

What's the difference between "sensitive to initial conditions" and "dependent on initial conditions"?

While similar, "sensitive to initial conditions" emphasizes the degree to which the system reacts to small changes, whereas "dependent on initial conditions" simply states that the initial state influences the outcome.

What does it mean for a system to be "dependent on initial conditions"?

It means the future state of the system is strongly influenced by its starting state. Small differences in the initial setup can result in large differences in the final outcome.

Are there situations where systems are not "dependent on initial conditions"?

Yes, some systems are more stable and predictable, meaning their outcomes are less sensitive to variations in their initial state. These systems are not considered "dependent on initial conditions".