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This work deals with the passive control-based chaos synchronization with circuit design for secure communication. First, the numerical simulation and electronic circuit design of a simple five-term chaotic system are performed. The numerical simulation and electronic circuit design outputs have confirmed each other. Then, the passive control method is applied for synchronizing two identical five-term chaotic systems using only one state control signal. After the synchronization study, design and analysis for secure communication by chaotic masking method are conducted in Matlab–Simulink platform. Finally, an electronic circuit design is performed for the designed communication system. In the designed communication system with Matlab–Simulink platform and electronic circuit design, information signal which is sent from the transmitter unit is successfully retrieved at the receiver unit. As a result, the electronic circuit design has shown that a single state passivity-based synchronization signal can be effectively used for secure data communication applications for the real environment.

In the paper, we futher consider a fractional-order system from a modified Chua’s circuit system with the smooth degree of 3 proposed by Fu et.al. Bifurcation analysis, multistability and coexisting attractors in the the fractional-order modified Chua’s circuit are studied. In addition, microcontroller-based circuit was implemented in real digital engineering applications by using the fractional-order Chua’s circuit with the piecewise-smooth continuous system.

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Recent evidence suggests that a system with only stable equilibria can generate chaotic behavior. In this work, we study a chaotic system with two stable equilibrium points. The dynamics of the system is investigated via phase portrait, bifurcation diagram and Lyapunov exponents. The feasibility of the system is introducing its electronic realization. Moreover, the chaotic system is used in Symmetric Chaos Shift Keying (SCSK) and Chaotic ON-OFF Keying (COOK) modulated communication designs for secure communication. It is determined that the SCSK modulated communication system implemented with the chaotic system is more successful than COOK modulation for secure communication.

An amplitude controllable hyperjerk system is constructed for chaos producing by introducing a nonlinear factor of memristor. In this case, the amplitude control is realized from a single coefficient in the memristor. The hyperjerk system has a line of equilibria and also shows extreme multistability indicated by the initial value-associated bifurcation diagram. FPGA-based circuit realization is also given for physical verification. Finally, the proposed memristive hyperjerk system is successfully predicted with artificial neural networks for AI based engineering applications.

By introducing a discrete memristor and periodic sinusoidal functions, a two-dimensional map with coexisting chaos and hyperchaos is constructed. Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are firstly found in this discrete map, along with which other regimes of coexistence such as coexisting chaos, quasi-periodic oscillation, and discrete periodic points are also captured. The hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants meanwhile the amplitude can also be controlled in combination with those coexisting attractors. Based on the nonlinear auto-regressive model with exogenous inputs (NARX) for neural network, the dynamics of the memristive map is well predicted, which provides a potential passage in artificial intelligence-based applications.

In this paper, we report a novel chaotic snap oscillator with one nonlinear function. Dynamic analysis of the system shows the existence of bistability. To study the time delay effects on the proposed snap oscillator, we introduce multiple time delay in the fourth state equation. Investigation of dynamical properties of the time-delayed system shows that the snap oscillator exhibits the same multistable properties as the nondelayed system. The new multistable hyperjerk chaotic system has been tested in chaos shift keying and symmetric choc shift keying modulated communication designs for engineering applications. It has been determined that the symmetric chaos shift keying modulated communication system implemented with the new chaotic system is more successful than the chaos shift keying modulation for secure communication. Also, circuit implementation of the chaotic snap oscillator with tangent function is carried out showing its feasibility.