गतिकीय तन्त्र
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गतिकीय तन्त्र (Dynamical system) ऐसी प्रक्रिया या गणितीय मॉडल जिसमें निहित चरों (स्टेट्स या अवस्थाएं) का मान समय पर निर्भर करता है तथा जिसमें निम्नलिखित दो गुण होते हैं:
- कारण-कार्य (causal) : भविष्य की अवस्थाएँ (चरों के मान) केवल वर्तमान ए॰ं भूत अवस्थाओं के उपर निर्भर हों।
- निर्धर्णीय (डिटरमिनिस्टिक) : भविष्य के किसी भी क्षण पर चरों का मान ए॰ और केवल ए॰ हो।
स्पष्टतः अप्रत्याशित (stochastic) तन्त्र व प्रायिकता (probability) पर आधारित तन्त्र गतिकीय तन्त्र की परिभाषा में नहीं आते। गणित, भौतिकी ए॰ं प्रौद्योगिकी में गतिकीय तन्त्र का कांसेप्ट बहुत ही उपयोगी है।
इन्हें भी देखें
- तन्त्र गतिकी (System dynamics)
- तन्त्र सिद्धान्त (Systems theory)
बाहरी कड़ियाँ
- Bouncing Ball
- Mechanical Strings
- Swinging Atwood's Machine (SAM)
- A collection of dynamic and non-linear system models and demo applets (in Monash University's Virtual Lab)
- Arxiv preprint server has daily submissions of (non-refereed) manuscripts in dynamical systems.
- DSWeb provides up-to-date information on dynamical systems and its applications.
- Encyclopedia of dynamical systems A part of Scholarpedia — peer reviewed and written by invited experts.
- Nonlinear Dynamics. Models of bifurcation and chaos by Elmer G. Wiens
- Oliver Knill has a series of examples of dynamical systems with explanations and interactive controls.
- Sci.Nonlinear FAQ 2.0 (Sept 2003) provides definitions, explanations and resources related to nonlinear science
- Online books or lecture notes
- Geometrical theory of dynamical systems. Nils Berglund's lecture notes for a course at ETH at the advanced undergraduate level.
- Dynamical systems. George D. Birkhoff's 1927 book already takes a modern approach to dynamical systems.
- Chaos: classical and quantum. An introduction to dynamical systems from the periodic orbit point of view.
- Modeling Dynamic Systems. An introduction to the development of mathematical models of dynamic systems.
- Learning Dynamical Systems. Tutorial on learning dynamical systems.
- Ordinary Differential Equations and Dynamical Systems. Lecture notes by Gerald Teschl
- Simulation software based on Dynamical Systems approach