In this work, we propose three chaotic (or hyperchaotic) models. These models are real or complex with one stable equilibrium point (hidden attractor). Based on a modified Sprott E model, three versions were introduced: the complex integer order, the real fractional order, and the complex fractional order. The basic properties of these models have been studied. We discover that the complex integer-order version has chaotic and hyperchaotic multi-scroll hidden attractors (MSHAs) by computing Lyapunov exponents (LEs). By making a small change to a model parameter, different MSHA values can be produced for this version. The dynamics of the real fractional version are investigated through a bifurcation diagram and LEs. It has chaotic hidden attractors for various fractional-order q values. Through varying the model parameters of the complex fractional-order (FO) version, different numbers of chaotic MSHAs can be generated. Due to the complex dynamic behaviours of the MSHAs, these models may have several applications in physics, secure communications, social relations and image encryption. A new kind of combination synchronization (CS) between one integer-order drive model and two FO response models with different dimensions is proposed. The tracking control method is used to investigate a scheme for this type of synchronization. As an example, we used our three models to test the validity of this scheme, and an agreement between the analytical and numerical results was found.

A new four-dimensional hyperchaotic model (4-DHM) with eight parameters is examined in this work. Depending on how two of these parameters are chosen, this model may contain equilibrium points or not. Therefore, we may choose a value that will make the corresponding attractor either hidden or self-excited. In this model, we consider the two scenarios and analyze the dynamics of the two instances. The numerical simulation of the novel 4-DHM is shown together with bifurcation diagrams, the Lyapunov exponent, and an examination of equilibrium and stability. The novel 4-DHM may be used in many science and engineering applications, such as electronic circuits and image encryption. A physical implementation is added to the electronic circuit’s MATLAB Simulink to confirm that the new 4-DHM can be built. The results of the numerical analysis and electronic circuit simulation of our model were in a good agreement. The color image’s encryption, decryption, histogram analysis, information entropy, correlation coefficient, number of pixels change rate, and unified average changing intensity are examined using the proposed model.