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<p>For difference equations of continuous argument of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(x(t + 1) = h(x(t)),\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mi>h</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(t \ge 0,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo>≥</mo> <mn>0</mn> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> where <i>h</i> is a piecewise linear function with hysteresis, we present and graphically illustrate two fundamentally different scenarios of the behavior of solutions: typical solutions are either asymptotically periodic and piecewise constant or strongly chaotic and asymptotic to functions that are discontinuous at every point.</p>

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DYNAMICS OF SOLUTIONS OF A CLASS OF PIECEWISE LINEAR DIFFERENCE EQUATIONS WITH HYSTERESIS

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Abdyvali Akbergenov,
  • Anatolii Dvornyk,
  • Olena Romanenko

摘要

For difference equations of continuous argument of the form \(x(t + 1) = h(x(t)),\) x ( t + 1 ) = h ( x ( t ) ) , \(t \ge 0,\) t ≥ 0 , where h is a piecewise linear function with hysteresis, we present and graphically illustrate two fundamentally different scenarios of the behavior of solutions: typical solutions are either asymptotically periodic and piecewise constant or strongly chaotic and asymptotic to functions that are discontinuous at every point.