| Summary: | The concepts of collectively accessible, collectively sensitive, collectively infinitely sensitive, and collectively Li–Yorke sensitive are defined in non-autonomous discrete systems. It is proved that, if the mapping sequence <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>h</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo>=</mo><mrow><mo stretchy="false">(</mo><msub><mi>h</mi><mn>1</mn></msub><mo>,</mo><msub><mi>h</mi><mn>2</mn></msub><mo>,</mo><mo>…</mo><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula> is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">W</mi></semantics></math></inline-formula>-chaotic, then <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>h</mi><mrow><mi>n</mi><mo>,</mo><mo>∞</mo></mrow></msub><mo>=</mo><mrow><mo stretchy="false">(</mo><msub><mi>h</mi><mi>n</mi></msub><mo>,</mo><msub><mi>h</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo stretchy="false">)</mo></mrow><mrow><mo stretchy="false">(</mo><mo>∀</mo><mi>n</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi><mo>=</mo><mrow><mo stretchy="false">{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo stretchy="false">}</mo></mrow><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula> would also be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">W</mi></semantics></math></inline-formula>-chaotic. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">W</mi></semantics></math></inline-formula>-chaos represents one of the following five properties: collectively accessible, sensitive, collectively sensitive, collectively infinitely sensitive, and collectively Li–Yorke sensitive. Then, the relationship of chaotic properties between the product system <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>H</mi><mn>1</mn></msub><mo>×</mo><msub><mi>H</mi><mn>2</mn></msub><mo>,</mo><msub><mi>f</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo>×</mo><msub><mi>g</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> and factor systems <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>H</mi><mn>1</mn></msub><mo>,</mo><msub><mi>f</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msub><mi>H</mi><mn>2</mn></msub><mo>,</mo><msub><mi>g</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> was presented. Furthermore, in this paper, it is also proved that, if the autonomous discrete system <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>X</mi><mo>,</mo><mover accent="true"><mi>h</mi><mo>^</mo></mover><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> induced by the <i>p</i>-periodic discrete system <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>H</mi><mo>,</mo><msub><mi>h</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">W</mi></semantics></math></inline-formula>-chaotic, then the <i>p</i>-periodic discrete system <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><mi>H</mi><mo>,</mo><msub><mi>f</mi><mrow><mn>1</mn><mo>,</mo><mo>∞</mo></mrow></msub><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> would also be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">W</mi></semantics></math></inline-formula>-chaotic.
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