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Weakly Delayed Linear Planar Systems of Discrete Equations
Halfarová, Hana ; Růžičková, Miroslava (oponent) ; Khusainov, Denys (oponent) ; Diblík, Josef (vedoucí práce)
The present thesis deals with planar weakly delayed linear discrete systems. The characteristic equations of weakly delayed systems are identical with those of the same systems but without delayed terms. In this case, after several steps, the space of solutions with a given starting dimension is pasted into a space with a dimension less than the starting one. In a sense, this situation is analogous to one known in the theory of linear differential systems with constant coefficients and special delays when the initially infinite dimensional space of solutions on the initial interval turns (after several steps) into a finite dimensional set of solutions. For every possible case, explicit general solutions are constructed and, finally, results on the dimensionality of the space of solutions are obtained. The stability of solutions is investigated as well.
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Weakly Delayed Linear Planar Systems of Discrete Equations
Halfarová, Hana ; Růžičková, Miroslava (oponent) ; Khusainov, Denys (oponent) ; Diblík, Josef (vedoucí práce)
The present thesis deals with planar weakly delayed linear discrete systems. The characteristic equations of weakly delayed systems are identical with those of the same systems but without delayed terms. In this case, after several steps, the space of solutions with a given starting dimension is pasted into a space with a dimension less than the starting one. In a sense, this situation is analogous to one known in the theory of linear differential systems with constant coefficients and special delays when the initially infinite dimensional space of solutions on the initial interval turns (after several steps) into a finite dimensional set of solutions. For every possible case, explicit general solutions are constructed and, finally, results on the dimensionality of the space of solutions are obtained. The stability of solutions is investigated as well.
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