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Chaos theory describes the behavior of certain dynamical systems – that is, systems whose state evolves with time – that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behavior of chaotic systems appears random. This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements involved. This behavior is known as deterministic chaos, or simply chaos.

Chaos theory describes the behavior of certain dynamical systems – that is, systems whose state evolves with time – that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behavior of chaotic systems appears random. This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements involved. This behavior is known as deterministic chaos, or simply chaos.

混沌理论描述了某些状态随时间演化的动力系统的行为，这些系统可能表现出对初始条件高度敏感的特点（通常被称为'''蝴蝶效应 Butterfly Effect'''）。由于扰动受初始条件影响而指数增长，因此混沌系统具有敏感性，敏感性使它的行为看起来是随机的。但是这种敏感性也会出现在确定的动力系统中，即<font color='blue'>它们</font>未来的动力<s>学</s>完全由它的初始条件定义，没有任何随机因素参与的系统中。这种现象被称为确定性混沌，或简单混沌。

混沌理论描述了某些状态随时间演化的动力系统的行为，这些系统可能表现出对初始条件高度敏感的特点（通常被称为'''蝴蝶效应 Butterfly Effect'''）。由于扰动受初始条件影响而指数增长，因此混沌系统具有敏感性，敏感性使它的行为看起来是随机的。但是这种敏感性也会出现在确定的动力系统中，即<font color='blue'>它们</font>未来的动力学<font color='blue'>变化</font>完全由它的初始条件定义，没有任何随机因素参与的系统中。这种现象被称为确定性混沌，或简单混沌。