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In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: selfexcited attractors and hidden attractors. The localization of selfexcited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with nonhyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phaselocked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with selfexcited attractors and hidden attractors.
new chaotic system  multiple attractors  electronic circuit realization  SBox algorithm  chaotic systems  circuit design  parameter estimation  optimization methods  Gaussian mixture model  chaotic system  empirical mode decomposition  permutation entropy  image encryption  hidden attractors  fixed point  stability  nonlinear transport equation  stochastic (strong) entropy solution  uniqueness  existence  multiscale multivariate entropy  multistability  selfreproducing system  chaos  hidden attractor  selfexcited attractor  fractional order  spectral entropy  coexistence  multistability  chaotic flow  hidden attractor  multistable  entropy  core entropy  Thurston’s algorithm  Hubbard tree  external rays  chaos  Lyapunov exponents  multiplevalued  static memory  strange attractors  fractional discrete chaos  entropy  projective synchronization  full state hybrid projective synchronization  generalized synchronization  inverse full state hybrid projective synchronization  inverse generalized synchronization  multichannel supply chain  service game  chaos  entropy  BOPS  Hopf bifurcation  selfexcited attractors  multistability  sample entropy  PRNG  Nonequilibrium fourdimensional chaotic system  entropy measure  adaptive approximatorbased control  neural network  uncertain dynamics  synchronization  fractionalorder  complexvariable chaotic system  unknown complex parameters  chaotic map  fixed point  chaos  approximate entropy  implementation  hidden attractor  hyperchaotic system  multistability  entropy analysis  hidden attractor  complex systems  fractionalorder  entropy  chaotic maps  chaos  spatial dynamics  Bogdanov Map  chaos  laser  resonator
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Image analysis is a fundamental task for extracting information from images acquired across a range of different devices. Since reliable quantitative results are requested, image analysis requires highly sophisticated numerical and analytical methods—particularly for applications in medicine, security, and remote sensing, where the results of the processing may consist of vitally important data. The contributions to this book provide a good overview of the most important demands and solutions concerning this research area. In particular, the reader will find image analysis applied for feature extraction, encryption and decryption of data, color segmentation, and in the support new technologies. In all the contributions, entropy plays a pivotal role.
image retrieval  multifeature fusion  entropy  relevance feedback  chaotic system  image encryption  permutationdiffusion  SHA256 hash value  dynamic index  entropy  keyframes  Shannon’s entropy  sign languages  video summarization  video skimming  image encryption  multipleimage encryption  twodimensional chaotic economic map  security analysis  image encryption  chaotic cryptography  cryptanalysis  chosenplaintext attack  image information entropy  blind image quality assessment (BIQA)  information entropy, natural scene statistics (NSS)  Weibull statistics  discrete cosine transform (DCT)  ultrasound  hepatic steatosis  Shannon entropy  fatty liver  metabolic syndrome  multiexposure image fusion  texture information entropy  adaptive selection  patch structure decomposition  image encryption  timedelay  random insertion  information entropy  chaotic map  uncertainty assessment  deep neural network  random forest  Shannon entropy  positron emission tomography  reconstruction  field of experts  additive manufacturing  3D prints  3D scanning  image entropy  depth maps  surface quality assessment  machine vision  image analysis  Arimoto entropy  freeform deformations  normalized divergence measure  gradient distributions  nonextensive entropy  nonrigid registration  pavement  macrotexture  3D digital imaging  entropy  decay trend  discrete entropy  infrared images  low contrast  multiscale tophat transform  image encryption  DNA encoding  chaotic cryptography  cryptanalysis  image privacy  computer aided diagnostics  colonoscopy  Rényi entropies  structural entropy  spatial filling factor  binary image  Cantor set  Hénon map  Minkowski island  primeindexed primes  Ramanujan primes  Kapur’s entropy  color image segmentation  whale optimization algorithm  differential evolution  hybrid algorithm  Otsu method  image encryption  dynamic filtering  DNA computing  3D Latin cube  permutation  diffusion  fuzzy entropy  electromagnetic field optimization  chaotic strategy  color image segmentation  multilevel thresholding  contrast enhancement  sigmoid  Tsallis statistics  qexponential  qsigmoid  qGaussian  ultrasound images  person reidentification  image analysis  hash layer  quantization loss  Hamming distance  crossentropy loss  image entropy  Shannon entropy  generalized entropies  image processing  image segmentation  medical imaging  remote sensing  security
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Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.
strongly regular graph  automorphism group  orbit matrix  binary polyhedral group  icosahedron  dodecahedron  600cell  Electric multiple unit trains  highlevel maintenance planning  time window  0–1 programming model  particle swarm algorithm  fixed point  splitquaternion  quadratic polynomial  splitoctonion  neutrosophic set  neutrosophic rough set  pessimistic (optimistic) multigranulation neutrosophic approximation operators  complete lattice  rough set  matroid  operator  attribute reduction  graded rough sets  rough intuitionistic fuzzy sets  dominance relation  logical conjunction operation  logical disjunction operation  multigranulation  planar point set  convex polygon  disjoint holes  fuzzy logic  pseudoBCI algebra  quasimaximal element  KGunion  quasialternating BCKalgebra  quality function deployment  engineering characteristics  group decision making  2tuple  metro station  emergency routes  graph partitioning  graph clustering  invariant measures  partition comparison  finite automorphism groups  graph automorphisms  Fuzzy sets  ring  normed space  fuzzy normed ring  fuzzy normed ideal  fuzzy implication  quantum Balgebra  qfilter  quotient algebra  basic implication algebra  Detour–Harary index  maximum  unicyclic  bicyclic  cacti  threeway decisions  intuitionistic fuzzy sets  multigranulation rough intuitionistic fuzzy sets  granularity importance degree  complexity  Chebyshev polynomials  gear graph  pyramid graphs  edge detection  Laplacian operation  regularization  parameter selection  performance evaluation  aggregation operator  triangular norm  ?convex set  atombond connectivity index  geometric arithmetic index  line graph  generalized bridge molecular graph  graceful labeling  edge graceful labeling  edge even graceful labeling  polar grid graph  graph  good drawing  crossing number  join product  cyclic permutation  nonlinear  synchronized  linear discrete  chaotic system  algorithm  generalized permanental polynomial  coefficient  copermanental  isoperimetric number  random graph  intersection graph  social network  Abel–Grassmann’s groupoid (AGgroupoid)  Abel–Grassmann’s group (AGgroup)  involution AGgroup  commutative group  filter  graceful labeling  edge even graceful labeling  cylinder grid graph  selective maintenance  multistate system  human reliability  optimization  genetic algorithm  hypernearring  multitransformation  embedding  distance matrix (spectrum)  distance signlees Laplacian matrix (spectrum)  (generalized) distance matrix  spectral radius  transmission regular graph  graph  good drawing  crossing number  join product  cyclic permutation  cyclic associative groupoid (CAgroupoid)  cancellative  variant CAgroupoids  decomposition theorem  construction methods
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