A new 3-D chaotic dynamical system with a peanut-shaped closed curve of equilibrium points is introduced in this work. Since the new chaotic system has infinite number of rest points, the new chaotic model exhibits hidden attractors. A detailed dynamic analysis of the new chaotic model using bifurcation diagrams and entropy analysis is described. The new nonlinear plant shows multi-stability and coexisting convergent attractors. A circuit model using MultiSim of the new 3-D chaotic model is designed for engineering applications. The new multi-stable chaotic system is simulated on a field-programmable gate array (FPGA) by applying two numerical methods, showing results in good agreement with numerical simulations. Consequently, we utilize the properties of our chaotic system in designing a new cipher colour image mechanism. Experimental results demonstrate the efficiency of the presented encryption mechanism, whose outcomes suggest promising applications for our chaotic system in various cryptographic applications.

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A 3-D Multi-Stable System With a Peanut-Shaped Equilibrium Curve: Circuit Design, FPGA Realization, and an Application to Image Encryption

Delay-induced periodic oscillation for fractional-order neural networks with mixed delays

Shunting inhibitory cellular neural networks with strongly unpredictable oscillations

M. Akhmet has been supported by a grant (118F161) from TUB¨ ˙ITAK,\nthe Scientific and Technological Research Council of Turkey.\nM. Tleubergenova and A. Zhamanshin have been supported in parts by the MES RK\ngrant (AP05132573) ”Cellular neural networks with continuous/discrete time and singular perturbations” (2018-2020). Republic of Kazakhstan.

Quasilinear differential equations with strongly unpredictable solutions

The existence and uniqueness of unpredictable solutions in the dynamics of nonhomogeneous linear systems of differential and discrete equations are investigated. The hyperbolic cases are under discussion. The presence of unpredictable solutions confirms the existence of Poincaré chaos. Simulations illustrating the chaos are provided.

Unpredictable solutions of linear differential and discrete equations

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Poincare chaos for a hyperbolic quasilinear system

In this paper, modulo periodic Poisson stable functions have been newly introduced. Quasilinear differential equations with modulo periodic Poisson stable coefficients are under investigation. The existence and uniqueness of asymptotically stable modulo periodic Poisson stable solutions have been proved. Numerical simulations, which illustrate the theoretical results are provided.

Akylbek Zhamanshin

Papers

Shunting inhibitory cellular neural networks with strongly unpredictable oscillations

Unpredictable solutions of linear differential and discrete equations

Quasilinear differential equations with strongly unpredictable solutions

Poincare chaos for a hyperbolic quasilinear system

Modulo Periodic Poisson Stable Solutions of Quasilinear Differential Equations.