Coexistence of generalized synchronization and inverse generalized synchronization between chaotic and hyperchaotic systems

In this paper, we present new schemes to synchronize different dimensional chaotic and hyperchaotic systems. Based on coexistence of generalized synchronization (GS) and inverse generalized synchronization (IGS), a new type of hybrid chaos synchronization is constructed. Using Lyapunov stability theory and stability theory of linear continuous-time systems, some sufficient conditions are derived to prove the coexistence of generalized synchronization and inverse generalized synchronization between 3D master chaotic system and 4D slave hyperchaotic system. Finally, two numerical examples are illustrated with the aim to show the effectiveness of the approaches developed herein

Coupled Maps with Growth and Death: An Approach to Cell Differentiation

An extension of coupled maps is given which allows for the growth of the number of elements, and is inspired by the cell differentiation problem. The growth of elements is made possible first by clustering the phases, and then by differentiating roles. The former leads to the time sharing of resources, while the latter leads to the separation of roles for the growth. The mechanism of the differentiation of elements is studied. An extension to a model with several internal phase variables is given, which shows differentiation of internal states. The relevance of interacting dynamics with internal states (``intra-inter" dynamics) to biological problems is discussed with an emphasis on heterogeneity by clustering, macroscopic robustness by partial synchronization and recursivity with the selection of initial conditions and digitalization.Comment: LatexText,figures are not included. submitted to PhysicaD (1995,revised 1996 May

Hidden homogeneous extreme multistability of a fractional-order hyperchaotic discrete-time system: chaos, initial offset boosting, amplitude control, control, and synchronization

Fractional order maps are a hot research topic; many new mathematical models are suitable for developing new applications in different areas of science and engineering. In this paper, a new class of a 2D fractional hyperchaotic map is introduced using the Caputo-like difference operator. The hyperchaotic map has no equilibrium and lines of equilibrium points, depending on the values of the system parameters. All of the chaotic attractors generated by the proposed fractional map are hidden. The system dynamics are analyzed via bifurcation diagrams, Lyapunov exponents, and phase portraits for different values of the fractional order. The results show that the fractional map has rich dynamical behavior, including hidden homogeneous multistability and offset boosting. The paper also illustrates a novel theorem, which assures that two hyperchaotic fractional discrete systems achieve synchronized dynamics using very simple linear control laws. Finally, the chaotic dynamics of the proposed system are stabilized at the origin via a suitable controller

A locally active discrete memristor model and its application in a hyperchaotic map

© 2022 Springer Nature Switzerland AG. Part of Springer Nature. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1007/s11071-021-07132-5The continuous memristor is a popular topic of research in recent years, however, there is rare discussion about the discrete memristor model, especially the locally active discrete memristor model. This paper proposes a locally active discrete memristor model for the first time and proves the three fingerprints characteristics of this model according to the definition of generalized memristor. A novel hyperchaotic map is constructed by coupling the discrete memristor with a two-dimensional generalized square map. The dynamical behaviors are analyzed with attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, and dynamic behavior distribution diagram. Numerical simulation analysis shows that there is significant improvement in the hyperchaotic area, the quasi-periodic area and the chaotic complexity of the two-dimensional map when applying the locally active discrete memristor. In addition, antimonotonicity and transient chaos behaviors of system are reported. In particular, the coexisting attractors can be observed in this discrete memristive system, resulting from the different initial values of the memristor. Results of theoretical analysis are well verified with hardware experimental measurements. This paper lays a great foundation for future analysis and engineering application of the discrete memristor and relevant the study of other hyperchaotic maps.Peer reviewedFinal Accepted Versio