The properties of a fractional-order memristor is studied, and the influences of parameters are analyzed and compared. The results reflect that the resistance value of a fractional-order memristor can be affected by fraction-order, frequency, the switch resistor ratio, average mobility and so on. In addition, the circuit of a fractional-order memristor that is serially connected and connected in parallel with inductance and capacitance are studied. Then, the current–voltage characteristics of a simple series one-port circuits that are composed of a fractional-order memristor and a capacitor, or composed of a fractional-order memristor and a inductor are studied separately. The results demonstrate that at the periodic excitation, the memristor in the series circuits will have capacitive properties or inductive properties as the fractional order changes, the dynamical properties can be used in a memristive circuit.
The mapping and projective method is extended to investigate a nonlinear (2 + 1)-dimensional coupled breaking system by introducing expansion and nonlinear transformation, and some exact propagating solutions with variable separation are constructed for the system. The propagating solitons are first observed by setting properly the arbitrary functions in the solutions. The different forms of multi-soliton evolution with Weierstrass p function could be achieved.
In order to solve the problem of group delay of filter design, this paper presents pre-distorted design method with Bessel function for coupled resonator filter and multiplexer with the maximally flat group delay characteristic. At the same time, the formulas and unitary parameter table of Bessel function has been gotten in this paper. The directly coupled resonator pass band filter and multiplexer can be achieved by using this approach. The design two examples are presented and the group delay is flat. The results validate its effectiveness.
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