Dynamic System
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A Dynamic System is a system that changes its internal state (in response to external stimuli and internal processes).
- Context:
- It can typically evolve System State through state transition and temporal progression.
- It can typically respond to Environmental Input through adaptive mechanisms and response functions.
- It can typically maintain System Stability through feedback loops and homeostatic processes.
- It can typically generate System Behavior through interaction patterns and emergent properties.
- It can typically transform System Component through dynamic reconfiguration and structural adaptation.
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- It can often exhibit System Trajectory along phase space and attractor states.
- It can often develop System Memory through hysteresis effects and path dependencies.
- It can often display System Oscillation between system states at characteristic frequencies.
- It can often undergo System Bifurcation at critical thresholds and tipping points.
- It can often demonstrate System Resilience against perturbations and disruptive events.
- ...
- It can range from being a Simple Dynamic System to being a Complex Dynamic System, depending on its component count and interaction complexity.
- It can range from being a Deterministic Dynamic System to being a Stochastic Dynamic System, depending on its predictability and randomness level.
- It can range from being a Linear Dynamic System to being a Nonlinear Dynamic System, depending on its response characteristics and state transition functions.
- It can range from being a Discrete Dynamic System to being a Continuous Dynamic System, depending on its state representation and time evolution.
- It can range from being a Stable Dynamic System to being a Chaotic Dynamic System, depending on its sensitivity to initial conditions and long-term predictability.
- It can range from being a Dynamic Physical System to being a Dynamic Abstract System, depending on its implementation domain.
- It can range from being a Fragile Dynamic System to being an Anti-Fragile Dynamic System, depending on its response to stress.
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- It can integrate with Measurement System for system monitoring and state observation.
- It can connect to Control System for system regulation and behavior modification.
- It can support Simulation System for system behavior prediction and scenario analysis.
- It can interact with Data Analysis System for system characteristic identification and pattern recognition.
- It can be represented by a Dynamic Temporal Dataset for system state tracking and behavioral analysis.
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- Examples:
- Physical Dynamic Systems, such as:
- Mechanical Dynamic Systems, such as:
- Fluid Dynamic Systems, such as:
- Biological Dynamic Systems, such as:
- Ecological Dynamic Systems, such as:
- Physiological Dynamic Systems, such as:
- Self-Replicating Systems, such as:
- Social Dynamic Systems, such as:
- Economic Dynamic Systems, such as:
- Organizational Dynamic Systems, such as:
- Computational Dynamic Systems, such as:
- ...
- Physical Dynamic Systems, such as:
- Counter-Examples:
- Static System, which lacks temporal evolution and state change capability.
- Equilibrium System, which maintains constant state without ongoing dynamic processes.
- Isolated System, which has no interaction with environment or external stimuli response.
- Purely Reactive System, which responds only to immediate stimuli without internal dynamic processes.
- Stable System at equilibrium point, such as a stopped clock without state variation.
- See: System Dynamics, Dynamical System Theory, Complex System, Adaptive System, Feedback System, State Space, Non-Linear System, Chaos Theory, Emergence, Self-Organization.
References
2014
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Dynamical_system Retrieved:2014-6-22.
- A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.
At any given time a dynamical system has a state given by a set of real numbers (a vector) that can be represented by a point in an appropriate state space (a geometrical manifold). Small changes in the state of the system create small changes in the numbers. The evolution rule of the dynamical system is a fixed rule that describes what future states follow from the current state. The rule is deterministic; in other words, for a given time interval only one future state follows from the current state.
- A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.