64 research outputs found
Continuous approximations of a class of piece-wise continuous systems
In this paper we provide a rigorous mathematical foundation for continuous
approximations of a class of systems with piece-wise continuous functions. By
using techniques from the theory of differential inclusions, the underlying
piece-wise functions can be locally or globally approximated. The approximation
results can be used to model piece-wise continuous-time dynamical systems of
integer or fractional-order. In this way, by overcoming the lack of numerical
methods for diffrential equations of fractional-order with discontinuous
right-hand side, unattainable procedures for systems modeled by this kind of
equations, such as chaos control, synchronization, anticontrol and many others,
can be easily implemented. Several examples are presented and three comparative
applications are studied.Comment: IJBC, accepted (examples revised
Synthesizing the L\"{u} attractor by parameter-switching
In this letter we synthesize numerically the L\"{u} attractor starting from
the generalized Lorenz and Chen systems, by switching the control parameter
inside a chosen finite set of values on every successive adjacent finite time
intervals. A numerical method with fixed step size for ODEs is used to
integrate the underlying initial value problem. As numerically and
computationally proved in this work, the utilized attractors synthesis
algorithm introduced by the present author before, allows to synthesize the
L\"{u} attractor starting from any finite set of parameter values.Comment: accepted IJBC, 15 pages, 5 figure
Parameter switching in a generalized Duffing system: Finding the stable attractors
This paper presents a simple periodic parameter-switching method which can
find any stable limit cycle that can be numerically approximated in a
generalized Duffing system. In this method, the initial value problem of the
system is numerically integrated and the control parameter is switched
periodically within a chosen set of parameter values. The resulted attractor
matches with the attractor obtained by using the average of the switched
values. The accurate match is verified by phase plots and Hausdorff distance
measure in extensive simulations
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