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第265行： − + + − − − − In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. [[File:Mathematical models for complex systems.jpg|thumb|Mathematical models for complex systems]] Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. [[File:Logical deterministic individual-based cellular automata model of single species population growth.gif|thumb|Logical deterministic individual-based cellular automata model of single species population growth]] Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical [[Cellular automaton|cellular automata]] are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical [[ontology]] of the object under study. The white-box modeling represents an automatic hyper-logical inference from the [[first principle]]s because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic [[axiomatic system]] of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem.<ref name="Kalmykov Lev V., Kalmykov Vyacheslav L. White-box model" /> − − }}</ref> In black-box models, the individual-based (mechanistic) mechanisms of a complex dynamic system remain hidden. Mathematical models for complex systems Black-box models are completely nonmechanistic. They are phenomenological and ignore a composition and internal structure of a complex system. We cannot investigate interactions of subsystems of such a non-transparent model. A white-box model of complex dynamic system has ‘transparent walls’ and directly shows underlying mechanisms. All events at micro-, meso- and macro-levels of a dynamic system are directly visible at all stages of its white-box model evolution. In most cases mathematical modelers use the heavy black-box mathematical methods, which cannot produce mechanistic models of complex dynamic systems. Grey-box models are intermediate and combine black-box and white-box approaches. Logical deterministic individual-based cellular automata model of single species population growth Creation of a white-box model of complex system is associated with the problem of the necessity of an a priori basic knowledge of the modeling subject. The deterministic logical cellular automata are necessary but not sufficient condition of a white-box model. The second necessary prerequisite of a white-box model is the presence of the physical ontology of the object under study. The white-box modeling represents an automatic hyper-logical inference from the first principles because it is completely based on the deterministic logic and axiomatic theory of the subject. The purpose of the white-box modeling is to derive from the basic axioms a more detailed, more concrete mechanistic knowledge about the dynamics of the object under study. The necessity to formulate an intrinsic axiomatic system of the subject before creating its white-box model distinguishes the cellular automata models of white-box type from cellular automata models based on arbitrary logical rules. If cellular automata rules have not been formulated from the first principles of the subject, then such a model may have a weak relevance to the real problem. − − } / ref − + − Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource − 对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型+
→复杂系统建模
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).<ref name="Kalmykov Lev V., Kalmykov Vyacheslav L. Solution">
Mathematical models of complex systems are of three types: black-box (phenomenological), white-box (mechanistic, based on the first principles) and grey-box (mixtures of phenomenological and mechanistic models).<ref name="Kalmykov Lev V., Kalmykov Vyacheslav L. Solution">
[[复杂系统]]的数学模型分为三种：'''黑箱 black-box'''（现象学），'''白箱 White box'''（力学，基于第一原理）和灰箱 grey-box（现象学和力学模型的混合）。在黑箱模型中，基于个体的复杂动态系统机制仍然是个谜。<ref name="Kalmykov Lev V., Kalmykov Vyacheslav L. Solution">Kalmykov, Lev V.; Kalmykov, Vyacheslav L. (2015), "A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata", Acta Biotheoretica, 63 (2): 1–19, doi:10.1007/s10441-015-9257-9, PMID 25980478, S2CID 2941481</ref> <ref name="A">Kalmykov, Lev V.; Kalmykov, Vyacheslav L. (2015), "A white-box model of S-shaped and double S-shaped single-species population growth", PeerJ, 3:e948: e948, doi:10.7717/peerj.948, PMC 4451025, PMID 26038717</ref>
[[复杂系统]]的数学模型分为三种：'''黑箱 black-box'''（现象学），'''白箱 White box'''（力学，基于第一原理）和灰箱 grey-box（现象学和力学模型的混合）。在黑箱模型中，基于个体的复杂动态系统机制仍然是个谜。<ref name="Kalmykov Lev V., Kalmykov Vyacheslav L. Solution">Kalmykov, Lev V.; Kalmykov, Vyacheslav L. (2015), "A Solution to the Biodiversity Paradox by Logical Deterministic Cellular Automata", Acta Biotheoretica, 63 (2): 1–19, doi:10.1007/s10441-015-9257-9, PMID 25980478, S2CID 2941481</ref>
<ref name="A">Kalmykov, Lev V.; Kalmykov, Vyacheslav L. (2015), "A white-box model of S-shaped and double S-shaped single-species population growth", PeerJ, 3:e948: e948, doi:10.7717/peerj.948, PMC 4451025, PMID 26038717</ref>
黑箱模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白箱模型是透明的，直接显示了潜在的机制。在动态系统白箱模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑箱方法，这些方法无法生成复杂动态系统的机械模型。灰箱模型是中间模型，结合了黑箱方法和白箱方法。
黑箱模型完全是非机械的。它们是现象学的，忽略了复杂系统的组成和内部结构。我们无法研究这种非透明模型的子系统之间的相互作用。复杂动态系统的白箱模型是透明的，直接显示了潜在的机制。在动态系统白箱模型演化的所有阶段，都可以直接看到微观、中观和宏观级别的所有事件。在大多数情况下，数学建模者使用纯数学的黑箱方法，这些方法无法生成复杂动态系统的机械模型。灰箱模型是中间模型，结合了黑箱方法和白箱方法。
复杂系统白箱模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白箱模型的必要条件，但不是充分条件。白箱模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白箱建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白箱建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白箱模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白箱类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。
复杂系统白箱模型的创建和先验的建模主体基础知识的必要性有关。确定性逻辑元胞自动机是白箱模型的必要条件，但不是充分条件。白箱模型的第二个必要先决条件是所研究对象的物理本体的存在。因为白箱建模完全基于主题的确定性逻辑和公理，因此，它代表了基于第一定律的自动超逻辑推断。白箱建模的目的是从基本公理中获得有关所研究对象动力学的更详细、更具体的机械知识。在创建对象的白箱模型之前必须制定对象的内在公理体系的必要性，可以根据任意逻辑规则将白箱类型的细胞自动机模型与细胞自动机模型区分开。如果尚未根据受试者的首要原理制定细胞自动机规则，则此类模型与实际问题的相关性可能较弱。<ref name="Kalmykov Lev V., Kalmykov Vyacheslav L. Solution"></ref>
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]
[[File:Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource.gif|thumb|Logical deterministic individual-based cellular automata model of interspecific competition for a single limited resource]]
对于单个有限资源，基于逻辑确定性个体的种间竞争元胞自动机模型。
==Hardware-based ("hard")硬件模拟（”硬“）==
==Hardware-based ("hard")硬件模拟（”硬“）==