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Chaos-based communications can be applied advantageously if the property of chaotic systems is suitably exploited. In this Letter a simple noncoherent detection method for chaos-shift-keying (CSK) modulation is proposed, exploiting some distinguishable property of chaotic maps for recovering the digital message. Specifically, the proposed method exploits the difference in the return maps of the signals representing the digital symbols. The determining parameter of the return maps is estimated using a simple regression algorithm. If the parameter strongly characterizes the chaotic map, the detection can achieve very good accuracy. This strong parametric characterization can be achieved by defining the regression model with only one parameter. Using the tent maps as chaos generators, the bit-error-rate under additive white Gaussian noise is studied by computer simulations.

As a powerful cryptanalysis tool, the method of return-map attacks can be used to extract secret messages masked by chaos in secure communication schemes. Recently, a simple defensive mechanism was presented to enhance the security of chaotic parameter modulation schemes against return-map attacks. Two techniques are combined in the proposed defensive mechanism: Multistep parameter modulation and alternative driving of two different transmitter variables. This paper restudies the security of this proposed defensive mechanism against return-map attacks, and points out that the security was much over-estimated in the original publication for both ciphertext-only attack and known/chosen-plaintext attacks. It is found that a deterministic relationship exists between the shape of the return map and the modulated parameter, and that such a relationship can be used to dramatically enhance return-map attacks thereby making them quite easy to break the defensive mechanism.

This paper introduces the complete bifurcation analysis in a PWM current-controlled H-Bridge inverter in a wide parameter space. First, we briefly explain the behavior of the waveform in the circuit in terms of the switched dynamical system. Then, the consecutive waveform during the duration of the clock interval is exactly discretized, and the return map is defined for the rigorous analysis. Using the map, we derive the one- and two-dimensional bifurcation diagrams, and discuss the specific property of each bifurcation phenomena in the circuit.

Recently, an effective method called return maps is proposed for the parameter estimation of chaotic systems. However, high time-consumption limits practical applications. In this paper, we focus on this problem, and an improved return maps method is proposed. It combines the differential evolution algorithm with the return maps method, and simplifies the calculation process of Euclidean distance. Numerical simulations are carried out on two fractional-order chaotic systems, and the other five methods are used as the comparison. Results show that the improved method can accurately estimate the parameters of chaotic systems, and it saves much time than does the classical return maps method. Furthermore, the proposed method also exhibits good anti-noise performance.

In this paper, we investigate the existence and number of crossing limit cycles in a class of planar piecewise linear systems with node–node type critical points defined in two zones separated by a nonregular line formed by two rays emanated from the origin $(0,0)$, which are the positive $x$- and $y$-axes. We focus our attention on the existence of two-point crossing limit cycles, which intersect the switching line at two points. We obtain sufficient conditions under which the system has two two-point crossing limit cycles which intersect only one of the two rays. Moreover, we construct examples to show that this class of systems can have two, three or four two-point crossing limit cycles.

As the novel types of chaos-generating circuit usable for the bio-inspired information processing with their simple and suitable structure for the integration, capacitor-transistor pair (CTP), return-map unit and CMOS chaos multivibrator (CMV) have been developed. Noise source for the Boltzmann machine utilizing CTP or CMV, and the coupling experiment with the return-map unit are discussed. Operation of the pipelined AD converter as the chaos generating circuit under the map function of the Bernoulli-shift is also demonstrated.