We consider shunting inhibitory cellular neural networks with inputs and outputs that are chaotic in a modified Li-Yorke sense. The original Li-Yorke definition of chaos has been modified such that infinitely many periodic motions separated from the motions of the scrambled set are now replaced with almost periodic ones. Another principal novelty of the paper is that chaos is obtained as soluti...

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynami...

This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of functions in an extended multifunction space (Sengupta and Ray, 2000), and the topological theory of convergence. Order, chaos, and complexity are described as dis...

Construction projects are often very complex and dynamic by their nature, and it is a well-known fact that such systems exist on the edge of chaos. The paper’s objective is to study construction projects poised on the edge of chaos and to explore the forces that may turn projects chaotic in the sense that the project crosses this dangerous edge. The prime aim is to understand how the phase tran...

Many physical theories like chaos theory are fundamentally concerned with the conceptual tension between determinism and randomness. Kolmogorov complexity can express randomness in determinism and gives an approach to formulate chaotic behavior.

Existing methods of complexity research are capable of describing certain specifics of bio systems over a given narrow range of parameters but often they cannot account for the initial emergence of complex biological systems, their evolution, state changes and sometimes-abrupt state transitions. Chaos tools have the potential of reaching to the essential driving mechanisms that organize matter ...

z y x − − = & ay x y + = & x b z ( − + = & (1) z c) Abstract – It is shown that symbolic sequence can be used to reconstruct a trajectory of a chaotic system with high precision. Examples of construction of symbolic sequence and trajectory reconstruction are given. A method that demonstrates exponential increase in precision with the length of processing is developed. Microtriode generator is d...

We study axisymmetric mean field spherical and spherical shell dynamo models, with both dynamic and algebraic α-quenchings. Our results show that there are qualitative as well as quantitative differences and similarities between these models. Regarding similarities, both groups of models exhibit symmetric, antisymmetric and mixed modes of behaviour. As regards differences, the important feature...

A bstract In this work, our prime objective is to study the phenomena of quantum chaos and complexity in machine learning dynamics Quantum Neural Network (QNN). Parameterized Circuits (PQCs) hybrid quantum-classical framework introduced as a universal function approximator perform optimization with Stochastic Gradient Descent (SGD). We employ statistical differential geometric approach theory Q...